Source: Official Guide for the GMAT 13th Ed. Problem Solving; #174 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #174


How many prime numbers between 1 and

How many prime numbers between 1 and 100 are factors of 7,150?

3 Explanations


Lucas Ignacio Maffioli

Hello, is there an easy way to find out that 11 and 13 are factors of 143.

I reached to 143 and considered it prime, how can I avoid this problem.


May 14, 2018 • Comment

Sam Kinsman, Magoosh Tutor

Hi Lucas,

Here, you really have to test different possible factors until you are sure that it is not divisible by any numbers aside from 1 and itself. I'd suggest that you start with 2, and move up until you get to a number, that multiplied by itself, is bigger than the number you are testing.

For example, if you are testing whether 97 is a prime number, you would test each number from 1 to 10. At 10, you know you can stop, because 10^2 is greater than 97.

You may also find the following list of divisibility rules helpful. I'd suggest that you learn the rules for 1 to 10.

May 14, 2018 • Reply



7 has a factor of 7
1000 has factors of 5^3, 2^3
150 has factors of 5^2, 2^1, 3^1
so total factors of 7150 is 5^5, 2^4, 3^1 and 7^1
Total 4 factors answer choice E.
But dint get 11 and 13 as factors instead i got 7 and 3

Please let me know were i went wrong

Thanks in advance:)

Dec 10, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Sonika,

In this question, we need to consider the prime factors of 7150. Seven, for example, is not a factor of 7150 (7150/7 is not an integer).

An efficient way to find the prime factors of a number is to use a factor tree, like Mike does in the explanation. Using this method, we find that the prime factorization of 7150 is


From this prime factorization, we can see that four prime numbers between 1 and 100 are factors of 7150:

2, 5, 11 and 13

I hope this clears up your doubts!

Dec 10, 2016 • Reply


Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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