What is the Greatest Common Factor of 75714 and 75726?

Greatest common factor (GCF) of 75714 and 75726 is 6.

GCF(75714,75726) = 6

We will now calculate the prime factors of 75714 and 75726, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75714 and 75726.

How to find the GCF of 75714 and 75726?

We will first find the prime factorization of 75714 and 75726. After we will calculate the factors of 75714 and 75726 and find the biggest common factor number .

Step-1: Prime Factorization of 75714

Prime factors of 75714 are 2, 3, 12619. Prime factorization of 75714 in exponential form is:

75714 = 2¹ × 3¹ × 12619¹

Step-2: Prime Factorization of 75726

Prime factors of 75726 are 2, 3, 7, 601. Prime factorization of 75726 in exponential form is:

75726 = 2¹ × 3² × 7¹ × 601¹

Step-3: Factors of 75714

List of positive integer factors of 75714 that divides 75714 without a remainder.

1, 2, 3, 6, 12619, 25238, 37857

Step-4: Factors of 75726

List of positive integer factors of 75726 that divides 75714 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 601, 1202, 1803, 3606, 4207, 5409, 8414, 10818, 12621, 25242, 37863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75714 and 75726. The biggest common factor number is the GCF number.
So the greatest common factor 75714 and 75726 is 6.

Also check out the Least Common Multiple of 75714 and 75726