What is the Greatest Common Factor of 67998 and 68016?

Greatest common factor (GCF) of 67998 and 68016 is 6.

GCF(67998,68016) = 6

We will now calculate the prime factors of 67998 and 68016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67998 and 68016.

How to find the GCF of 67998 and 68016?

We will first find the prime factorization of 67998 and 68016. After we will calculate the factors of 67998 and 68016 and find the biggest common factor number .

Step-1: Prime Factorization of 67998

Prime factors of 67998 are 2, 3, 7, 1619. Prime factorization of 67998 in exponential form is:

67998 = 2¹ × 3¹ × 7¹ × 1619¹

Step-2: Prime Factorization of 68016

Prime factors of 68016 are 2, 3, 13, 109. Prime factorization of 68016 in exponential form is:

68016 = 2⁴ × 3¹ × 13¹ × 109¹

Step-3: Factors of 67998

List of positive integer factors of 67998 that divides 67998 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1619, 3238, 4857, 9714, 11333, 22666, 33999

Step-4: Factors of 68016

List of positive integer factors of 68016 that divides 67998 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 109, 156, 208, 218, 312, 327, 436, 624, 654, 872, 1308, 1417, 1744, 2616, 2834, 4251, 5232, 5668, 8502, 11336, 17004, 22672, 34008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67998 and 68016. The biggest common factor number is the GCF number.
So the greatest common factor 67998 and 68016 is 6.

Also check out the Least Common Multiple of 67998 and 68016