What is the Greatest Common Factor of 45596 and 45600?

Greatest common factor (GCF) of 45596 and 45600 is 4.

GCF(45596,45600) = 4

We will now calculate the prime factors of 45596 and 45600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45596 and 45600.

How to find the GCF of 45596 and 45600?

We will first find the prime factorization of 45596 and 45600. After we will calculate the factors of 45596 and 45600 and find the biggest common factor number .

Step-1: Prime Factorization of 45596

Prime factors of 45596 are 2, 11399. Prime factorization of 45596 in exponential form is:

45596 = 2² × 11399¹

Step-2: 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-3: Factors of 45596

List of positive integer factors of 45596 that divides 45596 without a remainder.

1, 2, 4, 11399, 22798

Step-4: Factors of 45600

List of positive integer factors of 45600 that divides 45596 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45596 and 45600. The biggest common factor number is the GCF number.
So the greatest common factor 45596 and 45600 is 4.

Also check out the Least Common Multiple of 45596 and 45600