What is the Greatest Common Factor of 75700 and 75712?

Greatest common factor (GCF) of 75700 and 75712 is 4.

GCF(75700,75712) = 4

We will now calculate the prime factors of 75700 and 75712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75700 and 75712.

How to find the GCF of 75700 and 75712?

We will first find the prime factorization of 75700 and 75712. After we will calculate the factors of 75700 and 75712 and find the biggest common factor number .

Step-1: Prime Factorization of 75700

Prime factors of 75700 are 2, 5, 757. Prime factorization of 75700 in exponential form is:

75700 = 2² × 5² × 757¹

Step-2: 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-3: Factors of 75700

List of positive integer factors of 75700 that divides 75700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 757, 1514, 3028, 3785, 7570, 15140, 18925, 37850

Step-4: Factors of 75712

List of positive integer factors of 75712 that divides 75700 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75700 and 75712. The biggest common factor number is the GCF number.
So the greatest common factor 75700 and 75712 is 4.

Also check out the Least Common Multiple of 75700 and 75712