What is the Greatest Common Factor of 34665 and 34680?

Greatest common factor (GCF) of 34665 and 34680 is 15.

GCF(34665,34680) = 15

We will now calculate the prime factors of 34665 and 34680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34665 and 34680.

How to find the GCF of 34665 and 34680?

We will first find the prime factorization of 34665 and 34680. After we will calculate the factors of 34665 and 34680 and find the biggest common factor number .

Step-1: Prime Factorization of 34665

Prime factors of 34665 are 3, 5, 2311. Prime factorization of 34665 in exponential form is:

34665 = 3¹ × 5¹ × 2311¹

Step-2: Prime Factorization of 34680

Prime factors of 34680 are 2, 3, 5, 17. Prime factorization of 34680 in exponential form is:

34680 = 2³ × 3¹ × 5¹ × 17²

Step-3: Factors of 34665

List of positive integer factors of 34665 that divides 34665 without a remainder.

1, 3, 5, 15, 2311, 6933, 11555

Step-4: Factors of 34680

List of positive integer factors of 34680 that divides 34665 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34665 and 34680. The biggest common factor number is the GCF number.
So the greatest common factor 34665 and 34680 is 15.

Also check out the Least Common Multiple of 34665 and 34680