What is the Greatest Common Factor of 89600 and 89609?

Greatest common factor (GCF) of 89600 and 89609 is 1.

GCF(89600,89609) = 1

We will now calculate the prime factors of 89600 and 89609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89600 and 89609.

How to find the GCF of 89600 and 89609?

We will first find the prime factorization of 89600 and 89609. After we will calculate the factors of 89600 and 89609 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 89609

Prime factors of 89609 are 13, 61, 113. Prime factorization of 89609 in exponential form is:

89609 = 13¹ × 61¹ × 113¹

Step-3: Factors of 89600

List of positive integer factors of 89600 that divides 89600 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

Step-4: Factors of 89609

List of positive integer factors of 89609 that divides 89600 without a remainder.

1, 13, 61, 113, 793, 1469, 6893

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89600 and 89609. The biggest common factor number is the GCF number.
So the greatest common factor 89600 and 89609 is 1.

Also check out the Least Common Multiple of 89600 and 89609