What is the Greatest Common Factor of 75690 and 75710?

Greatest common factor (GCF) of 75690 and 75710 is 10.

GCF(75690,75710) = 10

We will now calculate the prime factors of 75690 and 75710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75690 and 75710.

How to find the GCF of 75690 and 75710?

We will first find the prime factorization of 75690 and 75710. After we will calculate the factors of 75690 and 75710 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 75710

Prime factors of 75710 are 2, 5, 67, 113. Prime factorization of 75710 in exponential form is:

75710 = 2¹ × 5¹ × 67¹ × 113¹

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 75710

List of positive integer factors of 75710 that divides 75690 without a remainder.

1, 2, 5, 10, 67, 113, 134, 226, 335, 565, 670, 1130, 7571, 15142, 37855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75690 and 75710. The biggest common factor number is the GCF number.
So the greatest common factor 75690 and 75710 is 10.

Also check out the Least Common Multiple of 75690 and 75710