Question

Find the greatest common factor of the pair of numbers.

104 and 260

A.
4

B.
13

C.
20

D.
52

Answer 1

52, so it's D.

Answer 2

but why 52?

Answer 3

@kamizamurai nice explanation!

To find the GCF of two (or more) numbers, write each one in its prime factorization. Then multiply together the largest common factor found in each factorization.

For example:
GCF(150,1750):
\[150=2*3*5*5 = 3^1*5^2\]\[1750=2*5*5*5*7 = 2^1*5^3*7^1\]\(3\) only appears in the factorization of \(75\), so we disregard it. Similarly, \(7\) only appears in the factorization of \(875\), so we disregard it as well. \(5\) appears in the factorization of both numbers, but the largest power of \(5\) they have in common is \(5^2\). \(2\) appears in the factorization of both numbers, with the largest power they have in common being \(2^1\). We multiply \(2^1* 5^2=2*5*5=50\) to get \(50\) as the GCF.