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## Comment on

2520k is a Perfect Square## Good evening!

My question might be ridiculous, but I got a bit confused and hope, you'll help me to figure the situation out.

Approaching this task, I was also relying on a rule of an even number of each prime in factorization. Thus, I thought, if a number is divisible by 5, it should be at least divisible by a square of 5 to satisfy the condition. However, it didn't lead me to a solution and I wonder why.

Thanks in advance for your answer :)

## You are absolutely right. We

You are absolutely right. We can already see that 2520k is divisible by 5, and since we're told that 2520k is a square, we can correctly conclude that 2520k is divisible by 5², which means there must be TWO 5's in the prime factorization of 2520k

Can you provide more details on the approach you took?

## I'm so sorry, only now I

## Ah, I can see how one might

Ah, I can see how one might interpret the question that way.

If that were the intent of an official GMAT question, there would definitely be some information that states that the variable represents a digit.

## is there a faster way to

## Great question.

Great question.

When using the ol' timey approach, try to find LARGE values that divide into the initial value.

For example, I know that 20 is a divisor of 2500, and 20 is a divisor of 20

So, 20 is a divisor of 2500 + 20 (aka 2520)

Se get: 2520 = (20)(126)

At this point, it's relatively easy to break down 20 and 126

Compare this to finding small values that divide into 2520

For example....

2520 = (2)(1260)

= (2)(2)(630)

= (2)(2)(3)(210)

etc...

Keep practicing your prime factorizing. You'll get faster!

Cheers,

Brent

## Thanks, Brent. I started with

## You know what they say: "Go

You know what they say: "Go big or go home" (I can only assume "they" are talking about prime factorization)

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