What is the Greatest Common Factor of 32100 and 32110?

Greatest common factor (GCF) of 32100 and 32110 is 10.

GCF(32100,32110) = 10

We will now calculate the prime factors of 32100 and 32110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32100 and 32110.

How to find the GCF of 32100 and 32110?

We will first find the prime factorization of 32100 and 32110. After we will calculate the factors of 32100 and 32110 and find the biggest common factor number .

Step-1: Prime Factorization of 32100

Prime factors of 32100 are 2, 3, 5, 107. Prime factorization of 32100 in exponential form is:

32100 = 2² × 3¹ × 5² × 107¹

Step-2: Prime Factorization of 32110

Prime factors of 32110 are 2, 5, 13, 19. Prime factorization of 32110 in exponential form is:

32110 = 2¹ × 5¹ × 13² × 19¹

Step-3: Factors of 32100

List of positive integer factors of 32100 that divides 32100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 107, 150, 214, 300, 321, 428, 535, 642, 1070, 1284, 1605, 2140, 2675, 3210, 5350, 6420, 8025, 10700, 16050

Step-4: Factors of 32110

List of positive integer factors of 32110 that divides 32100 without a remainder.

1, 2, 5, 10, 13, 19, 26, 38, 65, 95, 130, 169, 190, 247, 338, 494, 845, 1235, 1690, 2470, 3211, 6422, 16055

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32100 and 32110. The biggest common factor number is the GCF number.
So the greatest common factor 32100 and 32110 is 10.

Also check out the Least Common Multiple of 32100 and 32110