What is the Greatest Common Factor of 20625 and 20640?

Greatest common factor (GCF) of 20625 and 20640 is 15.

GCF(20625,20640) = 15

We will now calculate the prime factors of 20625 and 20640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20625 and 20640.

How to find the GCF of 20625 and 20640?

We will first find the prime factorization of 20625 and 20640. After we will calculate the factors of 20625 and 20640 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 20640

Prime factors of 20640 are 2, 3, 5, 43. Prime factorization of 20640 in exponential form is:

20640 = 2⁵ × 3¹ × 5¹ × 43¹

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 20640

List of positive integer factors of 20640 that divides 20625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 43, 48, 60, 80, 86, 96, 120, 129, 160, 172, 215, 240, 258, 344, 430, 480, 516, 645, 688, 860, 1032, 1290, 1376, 1720, 2064, 2580, 3440, 4128, 5160, 6880, 10320

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20625 and 20640. The biggest common factor number is the GCF number.
So the greatest common factor 20625 and 20640 is 15.

Also check out the Least Common Multiple of 20625 and 20640