What is the Greatest Common Factor of 65709 and 65714?

Greatest common factor (GCF) of 65709 and 65714 is 1.

GCF(65709,65714) = 1

We will now calculate the prime factors of 65709 and 65714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65709 and 65714.

How to find the GCF of 65709 and 65714?

We will first find the prime factorization of 65709 and 65714. After we will calculate the factors of 65709 and 65714 and find the biggest common factor number .

Step-1: Prime Factorization of 65709

Prime factors of 65709 are 3, 7, 149. Prime factorization of 65709 in exponential form is:

65709 = 3² × 7² × 149¹

Step-2: Prime Factorization of 65714

Prime factors of 65714 are 2, 11, 29, 103. Prime factorization of 65714 in exponential form is:

65714 = 2¹ × 11¹ × 29¹ × 103¹

Step-3: Factors of 65709

List of positive integer factors of 65709 that divides 65709 without a remainder.

1, 3, 7, 9, 21, 49, 63, 147, 149, 441, 447, 1043, 1341, 3129, 7301, 9387, 21903

Step-4: Factors of 65714

List of positive integer factors of 65714 that divides 65709 without a remainder.

1, 2, 11, 22, 29, 58, 103, 206, 319, 638, 1133, 2266, 2987, 5974, 32857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65709 and 65714. The biggest common factor number is the GCF number.
So the greatest common factor 65709 and 65714 is 1.

Also check out the Least Common Multiple of 65709 and 65714