(Remember to discuss this article on Diggwith your friends. You can also choose other bookmarking services from the Share / Save button at the bottom of this article.
After the most successful and very useful article on THE ULTIMATE GUIDE TO NUMBER CLASSIFICATION, LazyMaths.com is pleased to offer another path breaking article – THE ULTIMATE COLLECTION OF EVERY KNOWN TESTS OF DIVISIBILITY.
As a part of any speed math exam like GMAT, GRE or CAT, if you are trying to find out whether that number is evenly divisible without actually dividing it, then use these tests of divisibility. Learn these tests and save yourself precious time.
Divisor
Divisibility condition
Examples
1
Automatic
Every number is divisible by 1
2
The last digit is even (0,2,4,6 or 8 )
1294: 4 is even
3
The sum of digits is divisible by 3.
405: 4 + 0 + 5 = 9, which clearly is divisible by 3.
4
The number formed by the last two digits is divisible by 4.
40832: 32 is divisible by 4.
5
The last digit is 0 or 5.
490: the last digit is 0.
6
It is divisible by 2 and 3.
1,458: 1 + 4 + 5 + 8 = 18, 1 + 8 = 9, so it is divisible by 3 and the last digit is even, hence number is divisible 6.
7
If you double the last digit and subtract it from the rest of the number and the answer is divisible by 7.
483: 48 – (3 × 2) = 42 = 7 x 6.
8
The number formed by the last three digits is divisible by 8.
56: (5 × 2) + 6 = 16.
9
The sum of digits is divisible by 9.
2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9.
10
The number ends in 0.
130: the last digit is 0.
11
If you sum every second digit, and subtract all the other digits, the answer is divisible by 11.
918,082: 9 – 1 + 8 – 0 + 8 – 2 = 22.
12
The number is divisible by 3 and 4.
324: (32 × 2) − 4 = 60.
13
Add 4 times the last digit to the rest, the answer is divisible by 13.
637: 63 + (7 × 4) = 91, 9 + (1 × 4) = 13.
14
It is divisible by 2 and 7
224: it is divisible by 2 and by 7.
15
It is divisible by 3 and 5
390: it is divisible by 3 and by 5.
16
Sum the number with last two digits removed, times 4, plus the last two digits.
176: (1 × 4) + 76 = 80.
17
Subtract 5 times the last digit from the rest, the answer is divisible by 17.
221: 22 – (1 × 5) = 17.
18
It is divisible by 2 and 9.
342: it is divisible by 2 and by 9.
19
Add twice the last digit to the rest, the answer is divisible by 19.
437: 43 + (7 × 2) = 57.
20
The number formed by the last 2 digits is divisible by 20.
The number formed by the last two digits is divisible by 25.
134,250: 50 is divisible by 25.
27
Since 37×27=999; the multiplier is one, taking three digits at-a-time. Sum the digits in blocks of three from right to left.
2,644,272: 2 + 644 + 272 = 918.
Subtract 8 times the last digit from the rest.
621: 62 − (1×8) = 54.
29
Add three times the last digit to the rest.
261: 1×3=3; 3+26= 29
31
Subtract three times the last digit from the rest.
32
The number formed by the last five digits is divisible by 32, as follows:
If the ten thousands digit is even, examine the number formed by the last four digits.
41,312: 1312.
If the ten thousands digit is odd, examine the number formed by the last four digits plus 16.
254,176: 4176+16 = 4192.
Add the last two digits to 4 times the rest.
1,312: (13×4) + 12 = 64.
33
Add 10 times the last digit to the rest.
627: 62 + 7 x 10 = 132, 13 + 2 x 10 = 33.
37
Sum the digits in blocks of three from right to left. Since 37×27=999; round up to 1000; drop the three zeros; the multiplier is one, taking three digits at-a-time. Add these products, going from right to left. If the result is divisible by 37, then the number is divisible by 37.
This post is part of LazyMaths’ Math website review series. Dedicated purely to help math students, the review highlights tangible learning that the website offers to its visitors and users. If you would like to have your website considered for review, drop us an email – contact(at)lazymaths(dot)com.
Review in a Tweet
Comprehensive set of interactive math lessons, with unlimited practice
About the website AAA math features a comprehensive set of interactive math lessons, categorized well in terms of levels (Kindergarten through Eighth) or according to topics, like Addition, Algebra, Counting, Decimals, etc. This allows the user to use the site for class related work, as well as reviewing or learning any particular topic that he or she needs.
The most striking part of the website is the focus on interactivity. Fully interactive lessons enable illustration of key concepts through visual animation, reinforcement of important points through challenging fun math games, and prevention of learning of wrong ways of solving through immediate feedback. Also, interactivity engages the students, and makes learning math a fun activity.
Moreover, availability of unlimited practice questions allows the students to try out enough questions till they feel confident in a non-threatening environment. This has a huge impact on their self-esteem and confidence.
The content is available in two languages “English” as well as “Spanish”, allowing for a wider reach. Also, all the website content along with some additional stuff is available on a CD version. The CD version is completely advertisement free. It helps the students in avoiding distractions, and focus completely on learning.
What’s on the website?
AAAmath offers the following:
• A wide range (Kindergarten through Eighth) of lessons
• Unlimited practice questions on each topic
• Math Games
• Immediate feedback to the students
• Links to other mathematics resources
What’s the best part about this website?
No registration is required, and the site is very well structured, making navigation intuitive.
Any $$$?
Only if you buy the CD version – ranges from $24.95 to $240.95 depending on Home, Classroom or School editions
Review Disclaimer: This is an independent review of the given site. It only reflects the opinion of our site reviewer(s). Views and opinions expressed may not be representative of the site or its owners or its users and visitors. LazyMaths.com and its reviewer(s) cannot be held responsible for any damage caused to hardware or any other problem caused by visiting this site or misuse of this information. Any errors or omissions should be brought to our attention by contacting the site administrator.
Learning math on Twitter? Is this just a thought, a dream or mere wishful thinking? Not anymore!
LazyMaths.com has been sharing Free Speed Math shortcuts with its Twitter followers since the beginning of this year. Yes, One Free Shortcut a Day. Could it get better than this?
This has been so popular with our followers that they have been wanting for more! So, we plan to now offer something else for free too! More Math on Twitter!!
Starting June 15, we plan to offer one free Smart Math technique for our Twitter followers. If you are taking the GMAT, GRE, SAT, CAT, CET or any multiple choice based Math tests, this is an absolute must for you. All Smart Math techniques are in the Don’t Solve section of LazyMaths. The techniques are based on concepts of approximation, elimination and reverse substitution. Not only does using these techniques, save a ton of time to get to the answer, but it also helps in avoiding silly mistakes.
The Don’t Solve section contains problems in areas of Algebra, Percentages, Average, Ratio Proportion, Time, Speed & Distance, etc. Check out free samples here.
Eager to learn a new kind of Math right now? Go ahead, sign up with LazyMaths.com and select your choice of membership. We guarantee that you would not regret.
While we publish free speed math shortcuts and free smart math techniques, we also publish math puzzles, downloadable math learning resources like Number classification. All of these are available to our Twitter followers as well as on our blog – Zzzlog.
In short, learn math the web 2.0 way – right on Twitter! Simply follow LazyMaths on Twitter and become a pro in Twitter Math!!
This post is part of LazyMaths’ Math website review series. Dedicated purely to help math students, the review highlights tangible learning that the website offers to its visitors and users. If you would like to have your website considered for review, drop us an email - contact(at)lazymaths(dot)com.
Mathkinz.com – Rule the World (of Math)
Review in a Tweet –
By students for students – Download Math practice sheets for free from Mathkinz.com
About the website – Mathkinz is a unique site that’s entirely run and managed by kids. Yup, school kids of grades 4 through 8. They develop the content, in this case worksheets, test material, etc. and host it too!
The website was started by Nirlesh Jain, a father that takes keen interest in his kids’ education. While teaching his kids, he came up with the idea. After speaking to his friends and family, he gathered all the neighboring kids and encouraged them to start developing math content. And in just a few months, Mathkinz.com was born. To keep the interests of kids alive, he offers Mathkinz points for the content they develop. This encourages them to keep developing more content and also build up a competitive spirit amongst them.
Mathkinz also conducts Math competitions in the central New Jersey area to encourage local students to develop better math skills.
What’s on the website?
Mathkinz offers the following:
• An online Math Quiz (By Grades – 1 through 8 – US Standards)
• Math Practice sheets (By Grades – 1 through 8 & By Subjects )
• Math Jokes
• Math Games
• Math Resources (Other math websites links)
• Math News
• Math Forum (for parents to network, ask questions, provide suggestions, etc.)
What’s the best part about this website?
You don’t have to register or sign up. Just visit the site and start printing your Math worksheets at home for your kids!
Any $$$?
Mathkinz is free, yes really!!
Review Disclaimer: This is an independent review of the given site. It only reflects the opinion of our site reviewer(s). Views and opinions expressed may not be representative of the site or its owners or its users and visitors. LazyMaths.com and its reviewer(s) cannot be held responsible for any damage caused to hardware or any other problem caused by visiting this site or misuse of this information. Any errors or omissions should be brought to our attention by contacting the site administrator.
(Remember to Bookmark this article on Delicious for your future reference. You can also choose other bookmarking services from the Share / Save button at the bottom of this article.)
We have been using numbers in everyday life. Everything from 0 to 22/7 might sound the same to most, but numbers differ from one another. Based on their characteristics, they are classified in groups. Based on all the different types of numbers Mathematician’s have named, we have built the ultimate guide to Number classification.
The associated chart (at the bottom of the article) shows how the number groups are related to each other. Read below for more details on each number group.
Real Numbers – All kinds of numbers that you usually think of – from bus route numbers, to your weight, to pi and even the square root of pi! In short everything!! Everything? Really? Well…almost
Imaginary numbers – Have you ever tried finding the square root of -1? If you haven’t, try it on your calculator. It might show an error (if it is a dumb calc) or it might show an ‘i’. That little ‘i’ is called an imaginary number. In short square roots of negative numbers make imaginary numbers.
Complex Numbers – It’s rather simple! Make a combination of Real and Imaginary numbers and voila! You get a Complex number. Stuff like 3+2i or 3/4i make up complex numbers. Just think of it when you mix a real number with an imaginary one, things do get a bit complex!
Rational Numbers – Any number that can be written as a fraction is a rational number. So numbers like ½, ¾, even 22/7 and all integers are also rational numbers.
Irrational Numbers – Simply the opposite of rational numbers i.e. numbers that cannot be written as fraction, like square roots of prime numbers, the golden ratio, the real value of pi (22/7 is a mere approximation not the real value of pi) are irrational numbers.
Integers – Any number that is not a fraction and does not have a tail after the decimal point is an integer. This includes both negative as well as positive numbers as well as zero.
Fractions – Numbers that are expressed in a ratio are called fractions. This classification is based on the number arrangement and not the number value. Remember that even integers can be expressed as fractions – 3 = 6/2 so 6/2 is a fraction but 3 is not.
Proper Fractions – Whenever the value of the numerator in a fraction is less than the value of the denominator, it is called a proper fraction. i.e. it’s bottom heavy.
Improper Fractions – Whenever the value of the denominator in a fraction is less than the value of the numerator, it is called a proper fraction. i.e. it’s top heavy.
Mixed Fractions – All improper fractions can be converted into an integer with a proper fraction. This combination of an integer with a proper fraction is called a mixed fraction.
Natural Numbers – All positive integers (not including the zero) are Natural numbers. Simply put, whatever you can count in Nature uses a natural number.
Whole Numbers – All positive integers inclusive of the zero are Whole numbers. Not a big deal different from Natural numbers.
Even Numbers – All integers that end with a 0, 2, 4, 6, or 8 (including the numbers 0, 2, 4, 6 & 8 themselves) are even numbers. Note that ‘0’ itself is an even number. Also note that negative numbers can also be even so long as they can be integrally divided by 2.
Odd Numbers – All integers that are not even numbers are odd number
Prime Numbers – A natural number, more than one, which has exactly two distinct natural number divisors: 1 and itself – is called a Prime number. There can be infinite prime numbers.
Composite Numbers – A positive integer which has a positive divisor other than one or itself is a composite number. In other words, all numbers that are not prime are composite
Welcome to LazyMaths Blog -
The official home of the Fastest and Smartest Math around!
Check us out for some snappy Math ideas and witty Math quiz as you learn Math the intelligently lazy way!
We are the first and only website offering Speed Math shortcuts and Smart Math techniques.
Whether you are a School student taking a math test or the SAT or someone taking a competitive Math exam like GMAT, GRE or even the Math Olympiad, LazyMaths will boost your Math score and confidence.
Our students have reported getting 100% marks in their Math tests using our shortcuts and techniques!
for sharing and offline reading.
