What is the Greatest Common Factor of 89590 and 89600?

Greatest common factor (GCF) of 89590 and 89600 is 10.

GCF(89590,89600) = 10

We will now calculate the prime factors of 89590 and 89600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89590 and 89600.

How to find the GCF of 89590 and 89600?

We will first find the prime factorization of 89590 and 89600. After we will calculate the factors of 89590 and 89600 and find the biggest common factor number .

Step-1: Prime Factorization of 89590

Prime factors of 89590 are 2, 5, 17, 31. Prime factorization of 89590 in exponential form is:

89590 = 2¹ × 5¹ × 17² × 31¹

Step-2: Prime Factorization of 89600

Prime factors of 89600 are 2, 5, 7. Prime factorization of 89600 in exponential form is:

89600 = 2⁹ × 5² × 7¹

Step-3: Factors of 89590

List of positive integer factors of 89590 that divides 89590 without a remainder.

1, 2, 5, 10, 17, 31, 34, 62, 85, 155, 170, 289, 310, 527, 578, 1054, 1445, 2635, 2890, 5270, 8959, 17918, 44795

Step-4: Factors of 89600

List of positive integer factors of 89600 that divides 89590 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 128, 140, 160, 175, 200, 224, 256, 280, 320, 350, 400, 448, 512, 560, 640, 700, 800, 896, 1120, 1280, 1400, 1600, 1792, 2240, 2560, 2800, 3200, 3584, 4480, 5600, 6400, 8960, 11200, 12800, 17920, 22400, 44800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89590 and 89600. The biggest common factor number is the GCF number.
So the greatest common factor 89590 and 89600 is 10.

Also check out the Least Common Multiple of 89590 and 89600