What is the Greatest Common Factor of 30648 and 30660?

Greatest common factor (GCF) of 30648 and 30660 is 12.

GCF(30648,30660) = 12

We will now calculate the prime factors of 30648 and 30660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30648 and 30660.

How to find the GCF of 30648 and 30660?

We will first find the prime factorization of 30648 and 30660. After we will calculate the factors of 30648 and 30660 and find the biggest common factor number .

Step-1: Prime Factorization of 30648

Prime factors of 30648 are 2, 3, 1277. Prime factorization of 30648 in exponential form is:

30648 = 2³ × 3¹ × 1277¹

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 30648

List of positive integer factors of 30648 that divides 30648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1277, 2554, 3831, 5108, 7662, 10216, 15324

Step-4: Factors of 30660

List of positive integer factors of 30660 that divides 30648 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 30648 and 30660. The biggest common factor number is the GCF number.
So the greatest common factor 30648 and 30660 is 12.

Also check out the Least Common Multiple of 30648 and 30660