What is the Greatest Common Factor of 20688 and 20700?

Greatest common factor (GCF) of 20688 and 20700 is 12.

GCF(20688,20700) = 12

We will now calculate the prime factors of 20688 and 20700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20688 and 20700.

How to find the GCF of 20688 and 20700?

We will first find the prime factorization of 20688 and 20700. After we will calculate the factors of 20688 and 20700 and find the biggest common factor number .

Step-1: Prime Factorization of 20688

Prime factors of 20688 are 2, 3, 431. Prime factorization of 20688 in exponential form is:

20688 = 2⁴ × 3¹ × 431¹

Step-2: Prime Factorization of 20700

Prime factors of 20700 are 2, 3, 5, 23. Prime factorization of 20700 in exponential form is:

20700 = 2² × 3² × 5² × 23¹

Step-3: Factors of 20688

List of positive integer factors of 20688 that divides 20688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 431, 862, 1293, 1724, 2586, 3448, 5172, 6896, 10344

Step-4: Factors of 20700

List of positive integer factors of 20700 that divides 20688 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 25, 30, 36, 45, 46, 50, 60, 69, 75, 90, 92, 100, 115, 138, 150, 180, 207, 225, 230, 276, 300, 345, 414, 450, 460, 575, 690, 828, 900, 1035, 1150, 1380, 1725, 2070, 2300, 3450, 4140, 5175, 6900, 10350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20688 and 20700. The biggest common factor number is the GCF number.
So the greatest common factor 20688 and 20700 is 12.

Also check out the Least Common Multiple of 20688 and 20700