What is the Greatest Common Factor of 69360 and 69375?

Greatest common factor (GCF) of 69360 and 69375 is 15.

GCF(69360,69375) = 15

We will now calculate the prime factors of 69360 and 69375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69360 and 69375.

How to find the GCF of 69360 and 69375?

We will first find the prime factorization of 69360 and 69375. After we will calculate the factors of 69360 and 69375 and find the biggest common factor number .

Step-1: Prime Factorization of 69360

Prime factors of 69360 are 2, 3, 5, 17. Prime factorization of 69360 in exponential form is:

69360 = 2⁴ × 3¹ × 5¹ × 17²

Step-2: Prime Factorization of 69375

Prime factors of 69375 are 3, 5, 37. Prime factorization of 69375 in exponential form is:

69375 = 3¹ × 5⁴ × 37¹

Step-3: Factors of 69360

List of positive integer factors of 69360 that divides 69360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 34, 40, 48, 51, 60, 68, 80, 85, 102, 120, 136, 170, 204, 240, 255, 272, 289, 340, 408, 510, 578, 680, 816, 867, 1020, 1156, 1360, 1445, 1734, 2040, 2312, 2890, 3468, 4080, 4335, 4624, 5780, 6936, 8670, 11560, 13872, 17340, 23120, 34680

Step-4: Factors of 69375

List of positive integer factors of 69375 that divides 69360 without a remainder.

1, 3, 5, 15, 25, 37, 75, 111, 125, 185, 375, 555, 625, 925, 1875, 2775, 4625, 13875, 23125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69360 and 69375. The biggest common factor number is the GCF number.
So the greatest common factor 69360 and 69375 is 15.

Also check out the Least Common Multiple of 69360 and 69375