What is the Greatest Common Factor of 45600 and 45612?

Greatest common factor (GCF) of 45600 and 45612 is 12.

GCF(45600,45612) = 12

We will now calculate the prime factors of 45600 and 45612, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45600 and 45612.

How to find the GCF of 45600 and 45612?

We will first find the prime factorization of 45600 and 45612. After we will calculate the factors of 45600 and 45612 and find the biggest common factor number .

Step-1: Prime Factorization of 45600

Prime factors of 45600 are 2, 3, 5, 19. Prime factorization of 45600 in exponential form is:

45600 = 2⁵ × 3¹ × 5² × 19¹

Step-2: Prime Factorization of 45612

Prime factors of 45612 are 2, 3, 7, 181. Prime factorization of 45612 in exponential form is:

45612 = 2² × 3² × 7¹ × 181¹

Step-3: Factors of 45600

List of positive integer factors of 45600 that divides 45600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 25, 30, 32, 38, 40, 48, 50, 57, 60, 75, 76, 80, 95, 96, 100, 114, 120, 150, 152, 160, 190, 200, 228, 240, 285, 300, 304, 380, 400, 456, 475, 480, 570, 600, 608, 760, 800, 912, 950, 1140, 1200, 1425, 1520, 1824, 1900, 2280, 2400, 2850, 3040, 3800, 4560, 5700, 7600, 9120, 11400, 15200, 22800

Step-4: Factors of 45612

List of positive integer factors of 45612 that divides 45600 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 181, 252, 362, 543, 724, 1086, 1267, 1629, 2172, 2534, 3258, 3801, 5068, 6516, 7602, 11403, 15204, 22806

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45600 and 45612. The biggest common factor number is the GCF number.
So the greatest common factor 45600 and 45612 is 12.

Also check out the Least Common Multiple of 45600 and 45612