What is the Greatest Common Factor of 15714 and 15729?

Greatest common factor (GCF) of 15714 and 15729 is 3.

GCF(15714,15729) = 3

We will now calculate the prime factors of 15714 and 15729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15714 and 15729.

How to find the GCF of 15714 and 15729?

We will first find the prime factorization of 15714 and 15729. After we will calculate the factors of 15714 and 15729 and find the biggest common factor number .

Step-1: Prime Factorization of 15714

Prime factors of 15714 are 2, 3, 97. Prime factorization of 15714 in exponential form is:

15714 = 2¹ × 3⁴ × 97¹

Step-2: Prime Factorization of 15729

Prime factors of 15729 are 3, 7, 107. Prime factorization of 15729 in exponential form is:

15729 = 3¹ × 7² × 107¹

Step-3: Factors of 15714

List of positive integer factors of 15714 that divides 15714 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 97, 162, 194, 291, 582, 873, 1746, 2619, 5238, 7857

Step-4: Factors of 15729

List of positive integer factors of 15729 that divides 15714 without a remainder.

1, 3, 7, 21, 49, 107, 147, 321, 749, 2247, 5243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15714 and 15729. The biggest common factor number is the GCF number.
So the greatest common factor 15714 and 15729 is 3.

Also check out the Least Common Multiple of 15714 and 15729