What is the Greatest Common Factor of 69728 and 69732?

Greatest common factor (GCF) of 69728 and 69732 is 4.

GCF(69728,69732) = 4

We will now calculate the prime factors of 69728 and 69732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69728 and 69732.

How to find the GCF of 69728 and 69732?

We will first find the prime factorization of 69728 and 69732. After we will calculate the factors of 69728 and 69732 and find the biggest common factor number .

Step-1: Prime Factorization of 69728

Prime factors of 69728 are 2, 2179. Prime factorization of 69728 in exponential form is:

69728 = 2⁵ × 2179¹

Step-2: Prime Factorization of 69732

Prime factors of 69732 are 2, 3, 13, 149. Prime factorization of 69732 in exponential form is:

69732 = 2² × 3² × 13¹ × 149¹

Step-3: Factors of 69728

List of positive integer factors of 69728 that divides 69728 without a remainder.

1, 2, 4, 8, 16, 32, 2179, 4358, 8716, 17432, 34864

Step-4: Factors of 69732

List of positive integer factors of 69732 that divides 69728 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 149, 156, 234, 298, 447, 468, 596, 894, 1341, 1788, 1937, 2682, 3874, 5364, 5811, 7748, 11622, 17433, 23244, 34866

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69728 and 69732. The biggest common factor number is the GCF number.
So the greatest common factor 69728 and 69732 is 4.

Also check out the Least Common Multiple of 69728 and 69732