What is the Greatest Common Factor of 30960 and 30976?

Greatest common factor (GCF) of 30960 and 30976 is 16.

GCF(30960,30976) = 16

We will now calculate the prime factors of 30960 and 30976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30960 and 30976.

How to find the GCF of 30960 and 30976?

We will first find the prime factorization of 30960 and 30976. After we will calculate the factors of 30960 and 30976 and find the biggest common factor number .

Step-1: Prime Factorization of 30960

Prime factors of 30960 are 2, 3, 5, 43. Prime factorization of 30960 in exponential form is:

30960 = 2⁴ × 3² × 5¹ × 43¹

Step-2: Prime Factorization of 30976

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

30976 = 2⁸ × 11²

Step-3: Factors of 30960

List of positive integer factors of 30960 that divides 30960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 43, 45, 48, 60, 72, 80, 86, 90, 120, 129, 144, 172, 180, 215, 240, 258, 344, 360, 387, 430, 516, 645, 688, 720, 774, 860, 1032, 1290, 1548, 1720, 1935, 2064, 2580, 3096, 3440, 3870, 5160, 6192, 7740, 10320, 15480

Step-4: Factors of 30976

List of positive integer factors of 30976 that divides 30960 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30960 and 30976. The biggest common factor number is the GCF number.
So the greatest common factor 30960 and 30976 is 16.

Also check out the Least Common Multiple of 30960 and 30976