What is the Greatest Common Factor of 9100 and 9120?

Greatest common factor (GCF) of 9100 and 9120 is 20.

GCF(9100,9120) = 20

We will now calculate the prime factors of 9100 and 9120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9100 and 9120.

How to find the GCF of 9100 and 9120?

We will first find the prime factorization of 9100 and 9120. After we will calculate the factors of 9100 and 9120 and find the biggest common factor number .

Step-1: Prime Factorization of 9100

Prime factors of 9100 are 2, 5, 7, 13. Prime factorization of 9100 in exponential form is:

9100 = 2² × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 9120

Prime factors of 9120 are 2, 3, 5, 19. Prime factorization of 9120 in exponential form is:

9120 = 2⁵ × 3¹ × 5¹ × 19¹

Step-3: Factors of 9100

List of positive integer factors of 9100 that divides 9100 without a remainder.

1, 2, 4, 5, 7, 10, 13, 14, 20, 25, 26, 28, 35, 50, 52, 65, 70, 91, 100, 130, 140, 175, 182, 260, 325, 350, 364, 455, 650, 700, 910, 1300, 1820, 2275, 4550

Step-4: Factors of 9120

List of positive integer factors of 9120 that divides 9100 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9100 and 9120. The biggest common factor number is the GCF number.
So the greatest common factor 9100 and 9120 is 20.

Also check out the Least Common Multiple of 9100 and 9120