What is the Greatest Common Factor of 75712 and 75732?

Greatest common factor (GCF) of 75712 and 75732 is 4.

GCF(75712,75732) = 4

We will now calculate the prime factors of 75712 and 75732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75712 and 75732.

How to find the GCF of 75712 and 75732?

We will first find the prime factorization of 75712 and 75732. After we will calculate the factors of 75712 and 75732 and find the biggest common factor number .

Step-1: Prime Factorization of 75712

Prime factors of 75712 are 2, 7, 13. Prime factorization of 75712 in exponential form is:

75712 = 2⁶ × 7¹ × 13²

Step-2: Prime Factorization of 75732

Prime factors of 75732 are 2, 3, 6311. Prime factorization of 75732 in exponential form is:

75732 = 2² × 3¹ × 6311¹

Step-3: Factors of 75712

List of positive integer factors of 75712 that divides 75712 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 448, 676, 728, 832, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 5824, 9464, 10816, 18928, 37856

Step-4: Factors of 75732

List of positive integer factors of 75732 that divides 75712 without a remainder.

1, 2, 3, 4, 6, 12, 6311, 12622, 18933, 25244, 37866

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75712 and 75732. The biggest common factor number is the GCF number.
So the greatest common factor 75712 and 75732 is 4.

Also check out the Least Common Multiple of 75712 and 75732