What is the Greatest Common Factor of 30648 and 30654?

Greatest common factor (GCF) of 30648 and 30654 is 6.

GCF(30648,30654) = 6

We will now calculate the prime factors of 30648 and 30654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30648 and 30654.

How to find the GCF of 30648 and 30654?

We will first find the prime factorization of 30648 and 30654. After we will calculate the factors of 30648 and 30654 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 30654

Prime factors of 30654 are 2, 3, 13, 131. Prime factorization of 30654 in exponential form is:

30654 = 2¹ × 3² × 13¹ × 131¹

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 30654

List of positive integer factors of 30654 that divides 30648 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 131, 234, 262, 393, 786, 1179, 1703, 2358, 3406, 5109, 10218, 15327

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30648 and 30654. The biggest common factor number is the GCF number.
So the greatest common factor 30648 and 30654 is 6.

Also check out the Least Common Multiple of 30648 and 30654