What is the Greatest Common Factor of 45585 and 45600?

Greatest common factor (GCF) of 45585 and 45600 is 15.

GCF(45585,45600) = 15

We will now calculate the prime factors of 45585 and 45600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45585 and 45600.

How to find the GCF of 45585 and 45600?

We will first find the prime factorization of 45585 and 45600. After we will calculate the factors of 45585 and 45600 and find the biggest common factor number .

Step-1: Prime Factorization of 45585

Prime factors of 45585 are 3, 5, 1013. Prime factorization of 45585 in exponential form is:

45585 = 3² × 5¹ × 1013¹

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 45585

List of positive integer factors of 45585 that divides 45585 without a remainder.

1, 3, 5, 9, 15, 45, 1013, 3039, 5065, 9117, 15195

Step-4: Factors of 45600

List of positive integer factors of 45600 that divides 45585 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 45585 and 45600. The biggest common factor number is the GCF number.
So the greatest common factor 45585 and 45600 is 15.

Also check out the Least Common Multiple of 45585 and 45600