What is the Greatest Common Factor of 69600 and 69608?

Greatest common factor (GCF) of 69600 and 69608 is 8.

GCF(69600,69608) = 8

We will now calculate the prime factors of 69600 and 69608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69600 and 69608.

How to find the GCF of 69600 and 69608?

We will first find the prime factorization of 69600 and 69608. After we will calculate the factors of 69600 and 69608 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 69608

Prime factors of 69608 are 2, 7, 11, 113. Prime factorization of 69608 in exponential form is:

69608 = 2³ × 7¹ × 11¹ × 113¹

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 69608

List of positive integer factors of 69608 that divides 69600 without a remainder.

1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 113, 154, 226, 308, 452, 616, 791, 904, 1243, 1582, 2486, 3164, 4972, 6328, 8701, 9944, 17402, 34804

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69600 and 69608. The biggest common factor number is the GCF number.
So the greatest common factor 69600 and 69608 is 8.

Also check out the Least Common Multiple of 69600 and 69608