What is the Greatest Common Factor of 83584 and 83600?

Greatest common factor (GCF) of 83584 and 83600 is 16.

GCF(83584,83600) = 16

We will now calculate the prime factors of 83584 and 83600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83584 and 83600.

How to find the GCF of 83584 and 83600?

We will first find the prime factorization of 83584 and 83600. After we will calculate the factors of 83584 and 83600 and find the biggest common factor number .

Step-1: Prime Factorization of 83584

Prime factors of 83584 are 2, 653. Prime factorization of 83584 in exponential form is:

83584 = 2⁷ × 653¹

Step-2: Prime Factorization of 83600

Prime factors of 83600 are 2, 5, 11, 19. Prime factorization of 83600 in exponential form is:

83600 = 2⁴ × 5² × 11¹ × 19¹

Step-3: Factors of 83584

List of positive integer factors of 83584 that divides 83584 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 653, 1306, 2612, 5224, 10448, 20896, 41792

Step-4: Factors of 83600

List of positive integer factors of 83600 that divides 83584 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 19, 20, 22, 25, 38, 40, 44, 50, 55, 76, 80, 88, 95, 100, 110, 152, 176, 190, 200, 209, 220, 275, 304, 380, 400, 418, 440, 475, 550, 760, 836, 880, 950, 1045, 1100, 1520, 1672, 1900, 2090, 2200, 3344, 3800, 4180, 4400, 5225, 7600, 8360, 10450, 16720, 20900, 41800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83584 and 83600. The biggest common factor number is the GCF number.
So the greatest common factor 83584 and 83600 is 16.

Also check out the Least Common Multiple of 83584 and 83600