What is the Greatest Common Factor of 75296 and 75312?

Greatest common factor (GCF) of 75296 and 75312 is 16.

GCF(75296,75312) = 16

We will now calculate the prime factors of 75296 and 75312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75296 and 75312.

How to find the GCF of 75296 and 75312?

We will first find the prime factorization of 75296 and 75312. After we will calculate the factors of 75296 and 75312 and find the biggest common factor number .

Step-1: Prime Factorization of 75296

Prime factors of 75296 are 2, 13, 181. Prime factorization of 75296 in exponential form is:

75296 = 2⁵ × 13¹ × 181¹

Step-2: Prime Factorization of 75312

Prime factors of 75312 are 2, 3, 523. Prime factorization of 75312 in exponential form is:

75312 = 2⁴ × 3² × 523¹

Step-3: Factors of 75296

List of positive integer factors of 75296 that divides 75296 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 181, 208, 362, 416, 724, 1448, 2353, 2896, 4706, 5792, 9412, 18824, 37648

Step-4: Factors of 75312

List of positive integer factors of 75312 that divides 75296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 523, 1046, 1569, 2092, 3138, 4184, 4707, 6276, 8368, 9414, 12552, 18828, 25104, 37656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75296 and 75312. The biggest common factor number is the GCF number.
So the greatest common factor 75296 and 75312 is 16.

Also check out the Least Common Multiple of 75296 and 75312