What is the Greatest Common Factor of 20700 and 20709?

Greatest common factor (GCF) of 20700 and 20709 is 9.

GCF(20700,20709) = 9

We will now calculate the prime factors of 20700 and 20709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20700 and 20709.

How to find the GCF of 20700 and 20709?

We will first find the prime factorization of 20700 and 20709. After we will calculate the factors of 20700 and 20709 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 20709

Prime factors of 20709 are 3, 13, 59. Prime factorization of 20709 in exponential form is:

20709 = 3³ × 13¹ × 59¹

Step-3: Factors of 20700

List of positive integer factors of 20700 that divides 20700 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

Step-4: Factors of 20709

List of positive integer factors of 20709 that divides 20700 without a remainder.

1, 3, 9, 13, 27, 39, 59, 117, 177, 351, 531, 767, 1593, 2301, 6903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20700 and 20709. The biggest common factor number is the GCF number.
So the greatest common factor 20700 and 20709 is 9.

Also check out the Least Common Multiple of 20700 and 20709