What is the Greatest Common Factor of 75714 and 75729?

Greatest common factor (GCF) of 75714 and 75729 is 3.

GCF(75714,75729) = 3

We will now calculate the prime factors of 75714 and 75729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75714 and 75729.

How to find the GCF of 75714 and 75729?

We will first find the prime factorization of 75714 and 75729. After we will calculate the factors of 75714 and 75729 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 75729

Prime factors of 75729 are 3, 25243. Prime factorization of 75729 in exponential form is:

75729 = 3¹ × 25243¹

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 75729

List of positive integer factors of 75729 that divides 75714 without a remainder.

1, 3, 25243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75714 and 75729. The biggest common factor number is the GCF number.
So the greatest common factor 75714 and 75729 is 3.

Also check out the Least Common Multiple of 75714 and 75729