What is the Greatest Common Factor of 69587 and 69600?

Greatest common factor (GCF) of 69587 and 69600 is 1.

GCF(69587,69600) = 1

We will now calculate the prime factors of 69587 and 69600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69587 and 69600.

How to find the GCF of 69587 and 69600?

We will first find the prime factorization of 69587 and 69600. After we will calculate the factors of 69587 and 69600 and find the biggest common factor number .

Step-1: Prime Factorization of 69587

Prime factors of 69587 are 7, 9941. Prime factorization of 69587 in exponential form is:

69587 = 7¹ × 9941¹

Step-2: Prime Factorization of 69600

Prime factors of 69600 are 2, 3, 5, 29. Prime factorization of 69600 in exponential form is:

69600 = 2⁵ × 3¹ × 5² × 29¹

Step-3: Factors of 69587

List of positive integer factors of 69587 that divides 69587 without a remainder.

1, 7, 9941

Step-4: Factors of 69600

List of positive integer factors of 69600 that divides 69587 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 32, 40, 48, 50, 58, 60, 75, 80, 87, 96, 100, 116, 120, 145, 150, 160, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 480, 580, 600, 696, 725, 800, 870, 928, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2400, 2784, 2900, 3480, 4350, 4640, 5800, 6960, 8700, 11600, 13920, 17400, 23200, 34800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69587 and 69600. The biggest common factor number is the GCF number.
So the greatest common factor 69587 and 69600 is 1.

Also check out the Least Common Multiple of 69587 and 69600