What is the Greatest Common Factor of 67984 and 68004?

Greatest common factor (GCF) of 67984 and 68004 is 4.

GCF(67984,68004) = 4

We will now calculate the prime factors of 67984 and 68004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67984 and 68004.

How to find the GCF of 67984 and 68004?

We will first find the prime factorization of 67984 and 68004. After we will calculate the factors of 67984 and 68004 and find the biggest common factor number .

Step-1: Prime Factorization of 67984

Prime factors of 67984 are 2, 7, 607. Prime factorization of 67984 in exponential form is:

67984 = 2⁴ × 7¹ × 607¹

Step-2: Prime Factorization of 68004

Prime factors of 68004 are 2, 3, 1889. Prime factorization of 68004 in exponential form is:

68004 = 2² × 3² × 1889¹

Step-3: Factors of 67984

List of positive integer factors of 67984 that divides 67984 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 607, 1214, 2428, 4249, 4856, 8498, 9712, 16996, 33992

Step-4: Factors of 68004

List of positive integer factors of 68004 that divides 67984 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1889, 3778, 5667, 7556, 11334, 17001, 22668, 34002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67984 and 68004. The biggest common factor number is the GCF number.
So the greatest common factor 67984 and 68004 is 4.

Also check out the Least Common Multiple of 67984 and 68004