What is the Greatest Common Factor of 69664 and 69684?

Greatest common factor (GCF) of 69664 and 69684 is 4.

GCF(69664,69684) = 4

We will now calculate the prime factors of 69664 and 69684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69664 and 69684.

How to find the GCF of 69664 and 69684?

We will first find the prime factorization of 69664 and 69684. After we will calculate the factors of 69664 and 69684 and find the biggest common factor number .

Step-1: Prime Factorization of 69664

Prime factors of 69664 are 2, 7, 311. Prime factorization of 69664 in exponential form is:

69664 = 2⁵ × 7¹ × 311¹

Step-2: Prime Factorization of 69684

Prime factors of 69684 are 2, 3, 5807. Prime factorization of 69684 in exponential form is:

69684 = 2² × 3¹ × 5807¹

Step-3: Factors of 69664

List of positive integer factors of 69664 that divides 69664 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 311, 622, 1244, 2177, 2488, 4354, 4976, 8708, 9952, 17416, 34832

Step-4: Factors of 69684

List of positive integer factors of 69684 that divides 69664 without a remainder.

1, 2, 3, 4, 6, 12, 5807, 11614, 17421, 23228, 34842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69664 and 69684. The biggest common factor number is the GCF number.
So the greatest common factor 69664 and 69684 is 4.

Also check out the Least Common Multiple of 69664 and 69684