What is the Greatest Common Factor of 87584 and 87600?

Greatest common factor (GCF) of 87584 and 87600 is 16.

GCF(87584,87600) = 16

We will now calculate the prime factors of 87584 and 87600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 87584 and 87600.

How to find the GCF of 87584 and 87600?

We will first find the prime factorization of 87584 and 87600. After we will calculate the factors of 87584 and 87600 and find the biggest common factor number .

Step-1: Prime Factorization of 87584

Prime factors of 87584 are 2, 7, 17, 23. Prime factorization of 87584 in exponential form is:

87584 = 2⁵ × 7¹ × 17¹ × 23¹

Step-2: Prime Factorization of 87600

Prime factors of 87600 are 2, 3, 5, 73. Prime factorization of 87600 in exponential form is:

87600 = 2⁴ × 3¹ × 5² × 73¹

Step-3: Factors of 87584

List of positive integer factors of 87584 that divides 87584 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 23, 28, 32, 34, 46, 56, 68, 92, 112, 119, 136, 161, 184, 224, 238, 272, 322, 368, 391, 476, 544, 644, 736, 782, 952, 1288, 1564, 1904, 2576, 2737, 3128, 3808, 5152, 5474, 6256, 10948, 12512, 21896, 43792

Step-4: Factors of 87600

List of positive integer factors of 87600 that divides 87584 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 73, 75, 80, 100, 120, 146, 150, 200, 219, 240, 292, 300, 365, 400, 438, 584, 600, 730, 876, 1095, 1168, 1200, 1460, 1752, 1825, 2190, 2920, 3504, 3650, 4380, 5475, 5840, 7300, 8760, 10950, 14600, 17520, 21900, 29200, 43800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 87584 and 87600. The biggest common factor number is the GCF number.
So the greatest common factor 87584 and 87600 is 16.

Also check out the Least Common Multiple of 87584 and 87600