What is the Greatest Common Factor of 67986 and 68000?

Greatest common factor (GCF) of 67986 and 68000 is 2.

GCF(67986,68000) = 2

We will now calculate the prime factors of 67986 and 68000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67986 and 68000.

How to find the GCF of 67986 and 68000?

We will first find the prime factorization of 67986 and 68000. After we will calculate the factors of 67986 and 68000 and find the biggest common factor number .

Step-1: Prime Factorization of 67986

Prime factors of 67986 are 2, 3, 1259. Prime factorization of 67986 in exponential form is:

67986 = 2¹ × 3³ × 1259¹

Step-2: Prime Factorization of 68000

Prime factors of 68000 are 2, 5, 17. Prime factorization of 68000 in exponential form is:

68000 = 2⁵ × 5³ × 17¹

Step-3: Factors of 67986

List of positive integer factors of 67986 that divides 67986 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 1259, 2518, 3777, 7554, 11331, 22662, 33993

Step-4: Factors of 68000

List of positive integer factors of 68000 that divides 67986 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 125, 136, 160, 170, 200, 250, 272, 340, 400, 425, 500, 544, 680, 800, 850, 1000, 1360, 1700, 2000, 2125, 2720, 3400, 4000, 4250, 6800, 8500, 13600, 17000, 34000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67986 and 68000. The biggest common factor number is the GCF number.
So the greatest common factor 67986 and 68000 is 2.

Also check out the Least Common Multiple of 67986 and 68000