What is the Greatest Common Factor of 39584 and 39600?

Greatest common factor (GCF) of 39584 and 39600 is 16.

GCF(39584,39600) = 16

We will now calculate the prime factors of 39584 and 39600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39584 and 39600.

How to find the GCF of 39584 and 39600?

We will first find the prime factorization of 39584 and 39600. After we will calculate the factors of 39584 and 39600 and find the biggest common factor number .

Step-1: Prime Factorization of 39584

Prime factors of 39584 are 2, 1237. Prime factorization of 39584 in exponential form is:

39584 = 2⁵ × 1237¹

Step-2: Prime Factorization of 39600

Prime factors of 39600 are 2, 3, 5, 11. Prime factorization of 39600 in exponential form is:

39600 = 2⁴ × 3² × 5² × 11¹

Step-3: Factors of 39584

List of positive integer factors of 39584 that divides 39584 without a remainder.

1, 2, 4, 8, 16, 32, 1237, 2474, 4948, 9896, 19792

Step-4: Factors of 39600

List of positive integer factors of 39600 that divides 39584 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 48, 50, 55, 60, 66, 72, 75, 80, 88, 90, 99, 100, 110, 120, 132, 144, 150, 165, 176, 180, 198, 200, 220, 225, 240, 264, 275, 300, 330, 360, 396, 400, 440, 450, 495, 528, 550, 600, 660, 720, 792, 825, 880, 900, 990, 1100, 1200, 1320, 1584, 1650, 1800, 1980, 2200, 2475, 2640, 3300, 3600, 3960, 4400, 4950, 6600, 7920, 9900, 13200, 19800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39584 and 39600. The biggest common factor number is the GCF number.
So the greatest common factor 39584 and 39600 is 16.

Also check out the Least Common Multiple of 39584 and 39600