What is the Greatest Common Factor of 85584 and 85600?

Greatest common factor (GCF) of 85584 and 85600 is 16.

GCF(85584,85600) = 16

We will now calculate the prime factors of 85584 and 85600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85584 and 85600.

How to find the GCF of 85584 and 85600?

We will first find the prime factorization of 85584 and 85600. After we will calculate the factors of 85584 and 85600 and find the biggest common factor number .

Step-1: Prime Factorization of 85584

Prime factors of 85584 are 2, 3, 1783. Prime factorization of 85584 in exponential form is:

85584 = 2⁴ × 3¹ × 1783¹

Step-2: Prime Factorization of 85600

Prime factors of 85600 are 2, 5, 107. Prime factorization of 85600 in exponential form is:

85600 = 2⁵ × 5² × 107¹

Step-3: Factors of 85584

List of positive integer factors of 85584 that divides 85584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1783, 3566, 5349, 7132, 10698, 14264, 21396, 28528, 42792

Step-4: Factors of 85600

List of positive integer factors of 85600 that divides 85584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 107, 160, 200, 214, 400, 428, 535, 800, 856, 1070, 1712, 2140, 2675, 3424, 4280, 5350, 8560, 10700, 17120, 21400, 42800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85584 and 85600. The biggest common factor number is the GCF number.
So the greatest common factor 85584 and 85600 is 16.

Also check out the Least Common Multiple of 85584 and 85600