What is the Greatest Common Factor of 20700 and 20720?

Greatest common factor (GCF) of 20700 and 20720 is 20.

GCF(20700,20720) = 20

We will now calculate the prime factors of 20700 and 20720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20700 and 20720.

How to find the GCF of 20700 and 20720?

We will first find the prime factorization of 20700 and 20720. After we will calculate the factors of 20700 and 20720 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 20720

Prime factors of 20720 are 2, 5, 7, 37. Prime factorization of 20720 in exponential form is:

20720 = 2⁴ × 5¹ × 7¹ × 37¹

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 20720

List of positive integer factors of 20720 that divides 20700 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 37, 40, 56, 70, 74, 80, 112, 140, 148, 185, 259, 280, 296, 370, 518, 560, 592, 740, 1036, 1295, 1480, 2072, 2590, 2960, 4144, 5180, 10360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20700 and 20720. The biggest common factor number is the GCF number.
So the greatest common factor 20700 and 20720 is 20.

Also check out the Least Common Multiple of 20700 and 20720