What is the Greatest Common Factor of 75690 and 75700?

Greatest common factor (GCF) of 75690 and 75700 is 10.

GCF(75690,75700) = 10

We will now calculate the prime factors of 75690 and 75700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75690 and 75700.

How to find the GCF of 75690 and 75700?

We will first find the prime factorization of 75690 and 75700. After we will calculate the factors of 75690 and 75700 and find the biggest common factor number .

Step-1: Prime Factorization of 75690

Prime factors of 75690 are 2, 3, 5, 29. Prime factorization of 75690 in exponential form is:

75690 = 2¹ × 3² × 5¹ × 29²

Step-2: 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-3: Factors of 75690

List of positive integer factors of 75690 that divides 75690 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 29, 30, 45, 58, 87, 90, 145, 174, 261, 290, 435, 522, 841, 870, 1305, 1682, 2523, 2610, 4205, 5046, 7569, 8410, 12615, 15138, 25230, 37845

Step-4: Factors of 75700

List of positive integer factors of 75700 that divides 75690 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75690 and 75700. The biggest common factor number is the GCF number.
So the greatest common factor 75690 and 75700 is 10.

Also check out the Least Common Multiple of 75690 and 75700