Arthimetic Problem

GRE Quant Problem Solving
1

Question: 5 is the largest number that can divide evenly into both 25 and positive integer K, while 9 is the largest number that can divide evenly into both 81 and K. Which of the following is the largest possible number that could be divided into K and 270?

A.45
B.135
C.180
D.225
E.270

Comments:
This problem is from 3rd party material. I found the number’s value should be 45.

G.C.F. of (k,25) is 5. K should have one 5
G.C.F of (k,81) is 9. K Should have one 9

K should have 9^1 * 5^1 (3^2 * 5^1)

Prime factor of 270 - 2 * 3^3 * 5

A number x divides k and 270.

So i assumed n should have 3^2 * 5^1

But the official answer given in the booklet is 180.

Can anyone please explain?

2

@Leaderboard or @gregmat Can you please check and let me know if I solved correctly or the question is framed wrongly?

3

Perhaps the “largest” wording.

4

I guess both the question and answer is wrong. If n is largest (180) then it cannot divide k and 270 equally.

180’s factor is 2^2 * 3^2 * 5
270 factor is 2 * 3^3 * 5

We cannot have more 2 in denominator than the numerator as the question says it equally divides.

So the question shouldn’t mention largest n values and the official answer should be 45 instead of 180.

Thanks @ Leaderboard