What is the Greatest Common Factor of 35709 and 35724?

Greatest common factor (GCF) of 35709 and 35724 is 3.

GCF(35709,35724) = 3

We will now calculate the prime factors of 35709 and 35724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35709 and 35724.

How to find the GCF of 35709 and 35724?

We will first find the prime factorization of 35709 and 35724. After we will calculate the factors of 35709 and 35724 and find the biggest common factor number .

Step-1: Prime Factorization of 35709

Prime factors of 35709 are 3, 11903. Prime factorization of 35709 in exponential form is:

35709 = 3¹ × 11903¹

Step-2: Prime Factorization of 35724

Prime factors of 35724 are 2, 3, 13, 229. Prime factorization of 35724 in exponential form is:

35724 = 2² × 3¹ × 13¹ × 229¹

Step-3: Factors of 35709

List of positive integer factors of 35709 that divides 35709 without a remainder.

1, 3, 11903

Step-4: Factors of 35724

List of positive integer factors of 35724 that divides 35709 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 229, 458, 687, 916, 1374, 2748, 2977, 5954, 8931, 11908, 17862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35709 and 35724. The biggest common factor number is the GCF number.
So the greatest common factor 35709 and 35724 is 3.

Also check out the Least Common Multiple of 35709 and 35724