If p and q are positive integers, and 6pq^4 and 12p^2q^2 have a greatest common factor of 1,050, then which of the following is a possible value for the sum of p and q?
A. 6
B. 8
C. 12
D. 35
E. 42

Please explain.
The steps I took originally were dividing 1050 by 6 and 12.
To get pq^4 = 175
p^2q^2 = 87.5

Question

If p and q are positive integers, and 6pq^4 and 12p^2q^2 have a greatest common factor of 1,050, then which of the following is a possible value for the sum of p and q?
A. 6
B. 8
C. 12
D. 35
E. 42

Please explain.
The steps I took originally were dividing 1050 by 6 and 12.
To get pq^4 = 175
p^2q^2 = 87.5

tkhunny · Answer

6pq^4 = 6pq^2(q^2)
12p^2q^2 = 6pq^2(2p)
6pq^2 = 1050
Are we getting anywhere?

albert0898 · Answer

6pq^2 = 1050
Simplifies to pq^2 = 175

welshfella · Answer

and 7 * 5^2 = 175
so?

albert0898 · Answer

Where'd you get those numbers from?

albert0898 · Answer

Prime factoring?

welshfella · Answer

they are possible values of p and  q because they fit the identity

albert0898 · Answer

Okay! Now I understand this. Thank you!

welshfella · Answer

yw

tkhunny · Answer

Factoring.  It as ALL factoring.  There was nothing besides factoring.  Factor, factor, factor.