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?