What is the Greatest Common Factor of 69564 and 69584?

Greatest common factor (GCF) of 69564 and 69584 is 4.

GCF(69564,69584) = 4

We will now calculate the prime factors of 69564 and 69584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69564 and 69584.

How to find the GCF of 69564 and 69584?

We will first find the prime factorization of 69564 and 69584. After we will calculate the factors of 69564 and 69584 and find the biggest common factor number .

Step-1: Prime Factorization of 69564

Prime factors of 69564 are 2, 3, 11, 17, 31. Prime factorization of 69564 in exponential form is:

69564 = 2² × 3¹ × 11¹ × 17¹ × 31¹

Step-2: Prime Factorization of 69584

Prime factors of 69584 are 2, 4349. Prime factorization of 69584 in exponential form is:

69584 = 2⁴ × 4349¹

Step-3: Factors of 69564

List of positive integer factors of 69564 that divides 69564 without a remainder.

1, 2, 3, 4, 6, 11, 12, 17, 22, 31, 33, 34, 44, 51, 62, 66, 68, 93, 102, 124, 132, 186, 187, 204, 341, 372, 374, 527, 561, 682, 748, 1023, 1054, 1122, 1364, 1581, 2046, 2108, 2244, 3162, 4092, 5797, 6324, 11594, 17391, 23188, 34782

Step-4: Factors of 69584

List of positive integer factors of 69584 that divides 69564 without a remainder.

1, 2, 4, 8, 16, 4349, 8698, 17396, 34792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69564 and 69584. The biggest common factor number is the GCF number.
So the greatest common factor 69564 and 69584 is 4.

Also check out the Least Common Multiple of 69564 and 69584