What is the Greatest Common Factor of 69600 and 69610?

Greatest common factor (GCF) of 69600 and 69610 is 10.

GCF(69600,69610) = 10

We will now calculate the prime factors of 69600 and 69610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69600 and 69610.

How to find the GCF of 69600 and 69610?

We will first find the prime factorization of 69600 and 69610. After we will calculate the factors of 69600 and 69610 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 69610

Prime factors of 69610 are 2, 5, 6961. Prime factorization of 69610 in exponential form is:

69610 = 2¹ × 5¹ × 6961¹

Step-3: Factors of 69600

List of positive integer factors of 69600 that divides 69600 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

Step-4: Factors of 69610

List of positive integer factors of 69610 that divides 69600 without a remainder.

1, 2, 5, 10, 6961, 13922, 34805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69600 and 69610. The biggest common factor number is the GCF number.
So the greatest common factor 69600 and 69610 is 10.

Also check out the Least Common Multiple of 69600 and 69610