What is the Greatest Common Factor of 20625 and 20636?

Greatest common factor (GCF) of 20625 and 20636 is 11.

GCF(20625,20636) = 11

We will now calculate the prime factors of 20625 and 20636, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20625 and 20636.

How to find the GCF of 20625 and 20636?

We will first find the prime factorization of 20625 and 20636. After we will calculate the factors of 20625 and 20636 and find the biggest common factor number .

Step-1: Prime Factorization of 20625

Prime factors of 20625 are 3, 5, 11. Prime factorization of 20625 in exponential form is:

20625 = 3¹ × 5⁴ × 11¹

Step-2: Prime Factorization of 20636

Prime factors of 20636 are 2, 7, 11, 67. Prime factorization of 20636 in exponential form is:

20636 = 2² × 7¹ × 11¹ × 67¹

Step-3: Factors of 20625

List of positive integer factors of 20625 that divides 20625 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 125, 165, 275, 375, 625, 825, 1375, 1875, 4125, 6875

Step-4: Factors of 20636

List of positive integer factors of 20636 that divides 20625 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 67, 77, 134, 154, 268, 308, 469, 737, 938, 1474, 1876, 2948, 5159, 10318

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20625 and 20636. The biggest common factor number is the GCF number.
So the greatest common factor 20625 and 20636 is 11.

Also check out the Least Common Multiple of 20625 and 20636