What is the Greatest Common Factor of 64980 and 65000?

Greatest common factor (GCF) of 64980 and 65000 is 20.

GCF(64980,65000) = 20

We will now calculate the prime factors of 64980 and 65000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64980 and 65000.

How to find the GCF of 64980 and 65000?

We will first find the prime factorization of 64980 and 65000. After we will calculate the factors of 64980 and 65000 and find the biggest common factor number .

Step-1: Prime Factorization of 64980

Prime factors of 64980 are 2, 3, 5, 19. Prime factorization of 64980 in exponential form is:

64980 = 2² × 3² × 5¹ × 19²

Step-2: Prime Factorization of 65000

Prime factors of 65000 are 2, 5, 13. Prime factorization of 65000 in exponential form is:

65000 = 2³ × 5⁴ × 13¹

Step-3: Factors of 64980

List of positive integer factors of 64980 that divides 64980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 361, 380, 570, 684, 722, 855, 1083, 1140, 1444, 1710, 1805, 2166, 3249, 3420, 3610, 4332, 5415, 6498, 7220, 10830, 12996, 16245, 21660, 32490

Step-4: Factors of 65000

List of positive integer factors of 65000 that divides 64980 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 625, 650, 1000, 1250, 1300, 1625, 2500, 2600, 3250, 5000, 6500, 8125, 13000, 16250, 32500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64980 and 65000. The biggest common factor number is the GCF number.
So the greatest common factor 64980 and 65000 is 20.

Also check out the Least Common Multiple of 64980 and 65000