What is the Greatest Common Factor of 20657 and 20664?

Greatest common factor (GCF) of 20657 and 20664 is 7.

GCF(20657,20664) = 7

We will now calculate the prime factors of 20657 and 20664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20657 and 20664.

How to find the GCF of 20657 and 20664?

We will first find the prime factorization of 20657 and 20664. After we will calculate the factors of 20657 and 20664 and find the biggest common factor number .

Step-1: Prime Factorization of 20657

Prime factors of 20657 are 7, 13, 227. Prime factorization of 20657 in exponential form is:

20657 = 7¹ × 13¹ × 227¹

Step-2: Prime Factorization of 20664

Prime factors of 20664 are 2, 3, 7, 41. Prime factorization of 20664 in exponential form is:

20664 = 2³ × 3² × 7¹ × 41¹

Step-3: Factors of 20657

List of positive integer factors of 20657 that divides 20657 without a remainder.

1, 7, 13, 91, 227, 1589, 2951

Step-4: Factors of 20664

List of positive integer factors of 20664 that divides 20657 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 41, 42, 56, 63, 72, 82, 84, 123, 126, 164, 168, 246, 252, 287, 328, 369, 492, 504, 574, 738, 861, 984, 1148, 1476, 1722, 2296, 2583, 2952, 3444, 5166, 6888, 10332

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20657 and 20664. The biggest common factor number is the GCF number.
So the greatest common factor 20657 and 20664 is 7.

Also check out the Least Common Multiple of 20657 and 20664