What is the Greatest Common Factor of 69249 and 69264?

Greatest common factor (GCF) of 69249 and 69264 is 3.

GCF(69249,69264) = 3

We will now calculate the prime factors of 69249 and 69264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69249 and 69264.

How to find the GCF of 69249 and 69264?

We will first find the prime factorization of 69249 and 69264. After we will calculate the factors of 69249 and 69264 and find the biggest common factor number .

Step-1: Prime Factorization of 69249

Prime factors of 69249 are 3, 41, 563. Prime factorization of 69249 in exponential form is:

69249 = 3¹ × 41¹ × 563¹

Step-2: Prime Factorization of 69264

Prime factors of 69264 are 2, 3, 13, 37. Prime factorization of 69264 in exponential form is:

69264 = 2⁴ × 3² × 13¹ × 37¹

Step-3: Factors of 69249

List of positive integer factors of 69249 that divides 69249 without a remainder.

1, 3, 41, 123, 563, 1689, 23083

Step-4: Factors of 69264

List of positive integer factors of 69264 that divides 69249 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 37, 39, 48, 52, 72, 74, 78, 104, 111, 117, 144, 148, 156, 208, 222, 234, 296, 312, 333, 444, 468, 481, 592, 624, 666, 888, 936, 962, 1332, 1443, 1776, 1872, 1924, 2664, 2886, 3848, 4329, 5328, 5772, 7696, 8658, 11544, 17316, 23088, 34632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69249 and 69264. The biggest common factor number is the GCF number.
So the greatest common factor 69249 and 69264 is 3.

Also check out the Least Common Multiple of 69249 and 69264