What is the Greatest Common Factor of 30645 and 30660?

Greatest common factor (GCF) of 30645 and 30660 is 15.

GCF(30645,30660) = 15

We will now calculate the prime factors of 30645 and 30660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30645 and 30660.

How to find the GCF of 30645 and 30660?

We will first find the prime factorization of 30645 and 30660. After we will calculate the factors of 30645 and 30660 and find the biggest common factor number .

Step-1: Prime Factorization of 30645

Prime factors of 30645 are 3, 5, 227. Prime factorization of 30645 in exponential form is:

30645 = 3³ × 5¹ × 227¹

Step-2: Prime Factorization of 30660

Prime factors of 30660 are 2, 3, 5, 7, 73. Prime factorization of 30660 in exponential form is:

30660 = 2² × 3¹ × 5¹ × 7¹ × 73¹

Step-3: Factors of 30645

List of positive integer factors of 30645 that divides 30645 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 227, 681, 1135, 2043, 3405, 6129, 10215

Step-4: Factors of 30660

List of positive integer factors of 30660 that divides 30645 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 73, 84, 105, 140, 146, 210, 219, 292, 365, 420, 438, 511, 730, 876, 1022, 1095, 1460, 1533, 2044, 2190, 2555, 3066, 4380, 5110, 6132, 7665, 10220, 15330

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30645 and 30660. The biggest common factor number is the GCF number.
So the greatest common factor 30645 and 30660 is 15.

Also check out the Least Common Multiple of 30645 and 30660