What is the Greatest Common Factor of 75714 and 75732?

Greatest common factor (GCF) of 75714 and 75732 is 6.

GCF(75714,75732) = 6

We will now calculate the prime factors of 75714 and 75732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75714 and 75732.

How to find the GCF of 75714 and 75732?

We will first find the prime factorization of 75714 and 75732. After we will calculate the factors of 75714 and 75732 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 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 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 75732

List of positive integer factors of 75732 that divides 75714 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 75714 and 75732. The biggest common factor number is the GCF number.
So the greatest common factor 75714 and 75732 is 6.

Also check out the Least Common Multiple of 75714 and 75732