What is the Greatest Common Factor of 30660 and 30675?

Greatest common factor (GCF) of 30660 and 30675 is 15.

GCF(30660,30675) = 15

We will now calculate the prime factors of 30660 and 30675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30660 and 30675.

How to find the GCF of 30660 and 30675?

We will first find the prime factorization of 30660 and 30675. After we will calculate the factors of 30660 and 30675 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30675

Prime factors of 30675 are 3, 5, 409. Prime factorization of 30675 in exponential form is:

30675 = 3¹ × 5² × 409¹

Step-3: Factors of 30660

List of positive integer factors of 30660 that divides 30660 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

Step-4: Factors of 30675

List of positive integer factors of 30675 that divides 30660 without a remainder.

1, 3, 5, 15, 25, 75, 409, 1227, 2045, 6135, 10225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30660 and 30675. The biggest common factor number is the GCF number.
So the greatest common factor 30660 and 30675 is 15.

Also check out the Least Common Multiple of 30660 and 30675