What is the Greatest Common Factor of 67968 and 67978?

Greatest common factor (GCF) of 67968 and 67978 is 2.

GCF(67968,67978) = 2

We will now calculate the prime factors of 67968 and 67978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67968 and 67978.

How to find the GCF of 67968 and 67978?

We will first find the prime factorization of 67968 and 67978. After we will calculate the factors of 67968 and 67978 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67978

Prime factors of 67978 are 2, 41, 829. Prime factorization of 67978 in exponential form is:

67978 = 2¹ × 41¹ × 829¹

Step-3: Factors of 67968

List of positive integer factors of 67968 that divides 67968 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

Step-4: Factors of 67978

List of positive integer factors of 67978 that divides 67968 without a remainder.

1, 2, 41, 82, 829, 1658, 33989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67968 and 67978. The biggest common factor number is the GCF number.
So the greatest common factor 67968 and 67978 is 2.

Also check out the Least Common Multiple of 67968 and 67978