What is the Greatest Common Factor of 30978 and 30996?

Greatest common factor (GCF) of 30978 and 30996 is 18.

GCF(30978,30996) = 18

We will now calculate the prime factors of 30978 and 30996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30978 and 30996.

How to find the GCF of 30978 and 30996?

We will first find the prime factorization of 30978 and 30996. After we will calculate the factors of 30978 and 30996 and find the biggest common factor number .

Step-1: Prime Factorization of 30978

Prime factors of 30978 are 2, 3, 1721. Prime factorization of 30978 in exponential form is:

30978 = 2¹ × 3² × 1721¹

Step-2: Prime Factorization of 30996

Prime factors of 30996 are 2, 3, 7, 41. Prime factorization of 30996 in exponential form is:

30996 = 2² × 3³ × 7¹ × 41¹

Step-3: Factors of 30978

List of positive integer factors of 30978 that divides 30978 without a remainder.

1, 2, 3, 6, 9, 18, 1721, 3442, 5163, 10326, 15489

Step-4: Factors of 30996

List of positive integer factors of 30996 that divides 30978 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 41, 42, 54, 63, 82, 84, 108, 123, 126, 164, 189, 246, 252, 287, 369, 378, 492, 574, 738, 756, 861, 1107, 1148, 1476, 1722, 2214, 2583, 3444, 4428, 5166, 7749, 10332, 15498

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30978 and 30996. The biggest common factor number is the GCF number.
So the greatest common factor 30978 and 30996 is 18.

Also check out the Least Common Multiple of 30978 and 30996