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# [Smart Math] Algebra Problem 10

Here’s and example of a SMART MATH problem for ALGEBRA.

### Problem

What is the smallest number which 2880 must be divided by to make it a perfect square?

1. 3
2. 4
3. 5
4. 6
5. 8

### The Usual Method

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We first factorize 2880 to get the following factors:

$2880=2^{6}\times 3^{2}\times 5^{1}$

Hence, in order to make it to a perfect square, we have to divide 2880 by 5

$\frac{2880}{5}=2^{6}\times 3^{2}$

$\therefore \sqrt{2^{6}\times 3^{2}}=2^{3}\times 3^{1}=24$

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

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2880 can be split as a product of 288 and 10. 288 is a product of 2 and a perfect square 144. 10 is a product of 2 and 5. Hence, the only number that has a power of 1 is 5, so it has to be divided to make 2880 a perfect square.

(Ans: 3)

Estimated Time to arrive at the answer = 5 seconds.
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