What is the Greatest Common Factor of 67980 and 68000?

Greatest common factor (GCF) of 67980 and 68000 is 20.

GCF(67980,68000) = 20

We will now calculate the prime factors of 67980 and 68000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67980 and 68000.

How to find the GCF of 67980 and 68000?

We will first find the prime factorization of 67980 and 68000. After we will calculate the factors of 67980 and 68000 and find the biggest common factor number .

Step-1: Prime Factorization of 67980

Prime factors of 67980 are 2, 3, 5, 11, 103. Prime factorization of 67980 in exponential form is:

67980 = 2² × 3¹ × 5¹ × 11¹ × 103¹

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 67980

List of positive integer factors of 67980 that divides 67980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 103, 110, 132, 165, 206, 220, 309, 330, 412, 515, 618, 660, 1030, 1133, 1236, 1545, 2060, 2266, 3090, 3399, 4532, 5665, 6180, 6798, 11330, 13596, 16995, 22660, 33990

Step-4: Factors of 68000

List of positive integer factors of 68000 that divides 67980 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 67980 and 68000. The biggest common factor number is the GCF number.
So the greatest common factor 67980 and 68000 is 20.

Also check out the Least Common Multiple of 67980 and 68000