What is the Greatest Common Factor of 23100 and 23112?

Greatest common factor (GCF) of 23100 and 23112 is 12.

GCF(23100,23112) = 12

We will now calculate the prime factors of 23100 and 23112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23100 and 23112.

How to find the GCF of 23100 and 23112?

We will first find the prime factorization of 23100 and 23112. After we will calculate the factors of 23100 and 23112 and find the biggest common factor number .

Step-1: Prime Factorization of 23100

Prime factors of 23100 are 2, 3, 5, 7, 11. Prime factorization of 23100 in exponential form is:

23100 = 2² × 3¹ × 5² × 7¹ × 11¹

Step-2: Prime Factorization of 23112

Prime factors of 23112 are 2, 3, 107. Prime factorization of 23112 in exponential form is:

23112 = 2³ × 3³ × 107¹

Step-3: Factors of 23100

List of positive integer factors of 23100 that divides 23100 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 25, 28, 30, 33, 35, 42, 44, 50, 55, 60, 66, 70, 75, 77, 84, 100, 105, 110, 132, 140, 150, 154, 165, 175, 210, 220, 231, 275, 300, 308, 330, 350, 385, 420, 462, 525, 550, 660, 700, 770, 825, 924, 1050, 1100, 1155, 1540, 1650, 1925, 2100, 2310, 3300, 3850, 4620, 5775, 7700, 11550

Step-4: Factors of 23112

List of positive integer factors of 23112 that divides 23100 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 107, 108, 214, 216, 321, 428, 642, 856, 963, 1284, 1926, 2568, 2889, 3852, 5778, 7704, 11556

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23100 and 23112. The biggest common factor number is the GCF number.
So the greatest common factor 23100 and 23112 is 12.

Also check out the Least Common Multiple of 23100 and 23112