What is the Greatest Common Factor of 32100 and 32112?

Greatest common factor (GCF) of 32100 and 32112 is 12.

GCF(32100,32112) = 12

We will now calculate the prime factors of 32100 and 32112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32100 and 32112.

How to find the GCF of 32100 and 32112?

We will first find the prime factorization of 32100 and 32112. After we will calculate the factors of 32100 and 32112 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 32112

Prime factors of 32112 are 2, 3, 223. Prime factorization of 32112 in exponential form is:

32112 = 2⁴ × 3² × 223¹

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 32112

List of positive integer factors of 32112 that divides 32100 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 223, 446, 669, 892, 1338, 1784, 2007, 2676, 3568, 4014, 5352, 8028, 10704, 16056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32100 and 32112. The biggest common factor number is the GCF number.
So the greatest common factor 32100 and 32112 is 12.

Also check out the Least Common Multiple of 32100 and 32112