I have used LCM method:
for 7: it is only 7
for 150: it is 2*3*5*5
Distinct factors are 2,3,5 and 7
Hence option D

Please correct me if I am wrong.

LCM method is correct but 7150 is not divisible by 3 hence 3 cannot be considered as a prime number between 1 and 100.

It is not 7150 but 7 and 150

Oh yeah, but see the approach in both the numbers are same either it’s 7 and 150 or it’s 7150. The lcm method itself works.

Using prime factorization we get: 7,150 = (2)(5)(5)(11)(13)

So, FOUR prime numbers (2, 5, 11 and 13) are factors of 7,150

Answer: D

Cheers,
Brent

ASIDE: For anyone who feels that the correct answer should be E (since there are two 5's in the prime factorization of 7150), here's why the correct answer is actually D

The question starts with "How many prime numbers between 1 and 100..."
The prime numbers between 1 and 100 are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

"....are factors of 7,150"

So, how many numbers from the set {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} are factors of 7150?

The prime factors of 7150 are underlined {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} are factors of 7150

There are FOUR underlined primes

We need to find how many prime numbers between 1 and 100 are factors of 7,150

If you want to know what is a prime number then watch this video

Now, we can factorize 7150 to get

7150 = 715*10 = 5*143*5*2 = 5*11*13*5*2 = 2*\(5^2\)*11*13

Clearly, there are 4 prime numbers 2, 5, 11 and 13 which are between 1 and 100 and are factors of 7,150

So, Answer will be D.
Hope it helps!

Watch the following video to learn Basics of Prime Numbers




Watch the following video to learn How to find Prime Numbers from 1 to 100