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

1

How many prime numbers between 1 and

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

3 Explanations

1

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.

Thanks,
Lucas

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. https://brilliant.org/wiki/proof-of-divisibility-rules/

May 14, 2018 • Reply

1

SONIKA VASANTH

7150
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

2*5^2*11*13

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

1

Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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