What is the Greatest Common Factor of 30976 and 30984?

Greatest common factor (GCF) of 30976 and 30984 is 8.

GCF(30976,30984) = 8

We will now calculate the prime factors of 30976 and 30984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30976 and 30984.

How to find the GCF of 30976 and 30984?

We will first find the prime factorization of 30976 and 30984. After we will calculate the factors of 30976 and 30984 and find the biggest common factor number .

Step-1: Prime Factorization of 30976

Prime factors of 30976 are 2, 11. Prime factorization of 30976 in exponential form is:

30976 = 2⁸ × 11²

Step-2: Prime Factorization of 30984

Prime factors of 30984 are 2, 3, 1291. Prime factorization of 30984 in exponential form is:

30984 = 2³ × 3¹ × 1291¹

Step-3: Factors of 30976

List of positive integer factors of 30976 that divides 30976 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 128, 176, 242, 256, 352, 484, 704, 968, 1408, 1936, 2816, 3872, 7744, 15488

Step-4: Factors of 30984

List of positive integer factors of 30984 that divides 30976 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30976 and 30984. The biggest common factor number is the GCF number.
So the greatest common factor 30976 and 30984 is 8.

Also check out the Least Common Multiple of 30976 and 30984