What is the Greatest Common Factor of 67982 and 68000?

Greatest common factor (GCF) of 67982 and 68000 is 2.

GCF(67982,68000) = 2

We will now calculate the prime factors of 67982 and 68000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67982 and 68000.

How to find the GCF of 67982 and 68000?

We will first find the prime factorization of 67982 and 68000. After we will calculate the factors of 67982 and 68000 and find the biggest common factor number .

Step-1: Prime Factorization of 67982

Prime factors of 67982 are 2, 19, 1789. Prime factorization of 67982 in exponential form is:

67982 = 2¹ × 19¹ × 1789¹

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 67982

List of positive integer factors of 67982 that divides 67982 without a remainder.

1, 2, 19, 38, 1789, 3578, 33991

Step-4: Factors of 68000

List of positive integer factors of 68000 that divides 67982 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 67982 and 68000. The biggest common factor number is the GCF number.
So the greatest common factor 67982 and 68000 is 2.

Also check out the Least Common Multiple of 67982 and 68000