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Ans. For such questions plz follow the following technique.

The number of factors for a number say X is always equal to (a+1)(b+1)(c+1)..., where a,b,c,.. denote the power of the prime numbers that make this number.

Eg. 50 = 5 (Squared) * 2, here the prime numbers are 5 and 2, and their powers are 2 and 1 respectively. So a and b in this case are 2 and 1.

No of Factors of 50 = (2+1)(1+1) = 6

Similarly for ur question N, has 4 prime numbers as its factors.

Therefore number of Factors for N = (a+1)(b+1)(c+1)(d+1), given the options, a,b,c,d cannot take any other values except 1. SO the ans is 16.

Let me know if this is still not clear.
_________________

----------------------------------------------------------- 'It's not the ride, it's the rider'

I ll show you by an example lets say the number = 2*3*5*7 we need to find factors. clearly 1,2,3,5,7 are the factors. total number=5 now selecting the product 2 numbers at a time 4C2= 6 now selecting the product of 3 nos =4c3 =4 now the number n itself =1 sum it up = 16

There is a shorter methid If n= a^m * b^n * c^p and so on where a, b, c are the prime factors then total no of divisors= (m+1)*(n+1)*(p+1)

for eg here 2^1 * 3^1 * 5^1 *7^1 Total no of divisore = (1+1)(1+1)(1+1)(1+1)= 16

Thanks for the great explanation on factorization though.

Hey snoor Please dont gt confused ! 1 is STILL not a prime number. but 1 sure is a factor of any number, right? lets say n=2 It has 2 factors , 1 and itself

I ll show you by an example lets say the number = 2*3*5*7 we need to find factors. clearly 1,2,3,5,7 are the factors. total number=5 now selecting the product 2 numbers at a time 4C2= 6 now selecting the product of 3 nos =4c3 =4 now the number n itself =1 sum it up = 16

There is a shorter methid If n= a^m * b^n * c^p and so on where a, b, c are the prime factors then total no of divisors= (m+1)*(n+1)*(p+1)

for eg here 2^1 * 3^1 * 5^1 *7^1 Total no of divisore = (1+1)(1+1)(1+1)(1+1)= 16

cheers !!

thanks for the great explanation its very clear now
_________________

Ans. For such questions plz follow the following technique.

The number of factors for a number say X is always equal to (a+1)(b+1)(c+1)..., where a,b,c,.. denote the power of the prime numbers that make this number.

Eg. 50 = 5 (Squared) * 2, here the prime numbers are 5 and 2, and their powers are 2 and 1 respectively. So a and b in this case are 2 and 1.

No of Factors of 50 = (2+1)(1+1) = 6

Similarly for ur question N, has 4 prime numbers as its factors.

Therefore number of Factors for N = (a+1)(b+1)(c+1)(d+1), given the options, a,b,c,d cannot take any other values except 1. SO the ans is 16.

Let me know if this is still not clear.

Thanks for the great explanation its clear now
_________________

Thanks for the great explanation on factorization though.

Hey snoor Please dont gt confused ! 1 is STILL not a prime number. but 1 sure is a factor of any number, right? lets say n=2 It has 2 factors , 1 and itself

I think, it should be confused. Let see the original:

If positive number n is product of 4 different prime numbers, including 1 and n,.

I think, a. adding 1 and n to the total, so the total is 4 numbers. b. if the above statement is correct, 1 and n are not necessaryly prime number.

Thanks for the great explanation on factorization though.

Hey snoor Please dont gt confused ! 1 is STILL not a prime number. but 1 sure is a factor of any number, right? lets say n=2 It has 2 factors , 1 and itself

I think, it should be confused. Let see the original:

If positive number n is product of 4 different prime numbers, including 1 and n,.

I think, a. adding 1 and n to the total, so the total is 4 numbers. b. if the above statement is correct, 1 and n are not necessaryly prime number.

what do you think?

Hey there.. you might have to reinterpret that bit of the question stem that says "positive number n is product of 4 different prime numbers, including 1 and n, After all, a number that is a product of 4 prime numbers cannot be a prime number ! right? Question not framed well I guess. The factors would include 1 and n.

I agree with Sondenso, this question is not correct. GMAT would never include such ambiguous questions in exam.

Although the method everyone is trying to show here is correct (a+1)(b+1) ... but it doesn't apply to this qs as it stands. Whats the source of this qs vwdhawan1 ? Can you also post the explanation they give as the answer ?

Thanks for the great explanation on factorization though.

Hey snoor Please dont gt confused ! 1 is STILL not a prime number. but 1 sure is a factor of any number, right? lets say n=2 It has 2 factors , 1 and itself

I think, it should be confused. Let see the original:

If positive number n is product of 4 different prime numbers, including 1 and n,.

I think, a. adding 1 and n to the total, so the total is 4 numbers. b. if the above statement is correct, 1 and n are not necessaryly prime number.

what do you think?

THE QUESTION SHOULD READ AS UNDER: If positive integer n is the product of 4 different prime numbers, how many factors does n have, including 1 and n,?