If both 5 squared and 3 cubed...

[houstonrockets16]

If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3 , what is the smallest possible positive value of n?

A) 25
B) 27
C) 45
D) 75
E) 125

I am having trouble with this question....


I keep thinking it is A...

the correct answer is... D

Please help! Thanks!

[houstonrockets16]

n x 2^5 x 6^2 x 7^3 can be written as
n x 2^5 x (3 x 2)^2 x 7^3
= n x 2^7 x 3^2 x 7^3

This should contain atleast 2 factors of 5 (5^2) and 3 factors of 3(3^3). Since the number already has 2 factors of 3, the smallest possible value of n is 5^2 x 3 = 75

[NavdeepG]

since n multiplied by 2^5 x 6^2 x 7^3 already has 2 3's (6^2) as its prime factors, the only factors missing are one 3 and 2 5's.
Hence 3 * 5 * 5 = 75.

What is OA

[houstonrockets16]

75 is correct. Thanks

[clooner]

Anyone can explain this question to me? the solution in the book is to brief for me to understand. I mean I understand the math involved but I can't get my head around the first step!

[MBA.Aspirant]

If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3 , what is the smallest possible positive value of n?

A) 25
B) 27
C) 45
D) 75
E) 125

prime factorize

n x 2^5 x 6^2 x 7^3

n x 2^5 x (2^2 x 3^2) x 7^3

since 3^3 and 5^2 are factors of this, and 3^2 is also included in it, then what remains is 3 and 5^2

so n = 3 * 5^2 = 75

[clooner]

prime factorize

n x 2^5 x 6^2 x 7^3

n x 2^5 x (2^2 x 3^2) x 7^3

since 3^3 and 5^2 are factors of this, and 3^2 is also included in it, then what remains is 3 and 5^2

so n = 3 * 5^2 = 75

Thanks for the quick reply. My first language is not English and I think the problem is not that I don't get the math but that I don't understand what is asked. The question doesn't make sense to me at all. Maybe you or someone has another question with the same problem which I can try to solve. I'm starring blind on this one.