What is the Greatest Common Factor of 67956 and 67968?

Greatest common factor (GCF) of 67956 and 67968 is 12.

GCF(67956,67968) = 12

We will now calculate the prime factors of 67956 and 67968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67956 and 67968.

How to find the GCF of 67956 and 67968?

We will first find the prime factorization of 67956 and 67968. After we will calculate the factors of 67956 and 67968 and find the biggest common factor number .

Step-1: Prime Factorization of 67956

Prime factors of 67956 are 2, 3, 7, 809. Prime factorization of 67956 in exponential form is:

67956 = 2² × 3¹ × 7¹ × 809¹

Step-2: Prime Factorization of 67968

Prime factors of 67968 are 2, 3, 59. Prime factorization of 67968 in exponential form is:

67968 = 2⁷ × 3² × 59¹

Step-3: Factors of 67956

List of positive integer factors of 67956 that divides 67956 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 809, 1618, 2427, 3236, 4854, 5663, 9708, 11326, 16989, 22652, 33978

Step-4: Factors of 67968

List of positive integer factors of 67968 that divides 67956 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64, 72, 96, 118, 128, 144, 177, 192, 236, 288, 354, 384, 472, 531, 576, 708, 944, 1062, 1152, 1416, 1888, 2124, 2832, 3776, 4248, 5664, 7552, 8496, 11328, 16992, 22656, 33984

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67956 and 67968. The biggest common factor number is the GCF number.
So the greatest common factor 67956 and 67968 is 12.

Also check out the Least Common Multiple of 67956 and 67968