What is the Greatest Common Factor of 30960 and 30964?

Greatest common factor (GCF) of 30960 and 30964 is 4.

GCF(30960,30964) = 4

We will now calculate the prime factors of 30960 and 30964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30960 and 30964.

How to find the GCF of 30960 and 30964?

We will first find the prime factorization of 30960 and 30964. After we will calculate the factors of 30960 and 30964 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 30964

Prime factors of 30964 are 2, 7741. Prime factorization of 30964 in exponential form is:

30964 = 2² × 7741¹

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 30964

List of positive integer factors of 30964 that divides 30960 without a remainder.

1, 2, 4, 7741, 15482

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30960 and 30964. The biggest common factor number is the GCF number.
So the greatest common factor 30960 and 30964 is 4.

Also check out the Least Common Multiple of 30960 and 30964