What is the Greatest Common Factor of 65985 and 66000?

Greatest common factor (GCF) of 65985 and 66000 is 15.

GCF(65985,66000) = 15

We will now calculate the prime factors of 65985 and 66000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65985 and 66000.

How to find the GCF of 65985 and 66000?

We will first find the prime factorization of 65985 and 66000. After we will calculate the factors of 65985 and 66000 and find the biggest common factor number .

Step-1: Prime Factorization of 65985

Prime factors of 65985 are 3, 5, 53, 83. Prime factorization of 65985 in exponential form is:

65985 = 3¹ × 5¹ × 53¹ × 83¹

Step-2: Prime Factorization of 66000

Prime factors of 66000 are 2, 3, 5, 11. Prime factorization of 66000 in exponential form is:

66000 = 2⁴ × 3¹ × 5³ × 11¹

Step-3: Factors of 65985

List of positive integer factors of 65985 that divides 65985 without a remainder.

1, 3, 5, 15, 53, 83, 159, 249, 265, 415, 795, 1245, 4399, 13197, 21995

Step-4: Factors of 66000

List of positive integer factors of 66000 that divides 65985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 125, 132, 150, 165, 176, 200, 220, 240, 250, 264, 275, 300, 330, 375, 400, 440, 500, 528, 550, 600, 660, 750, 825, 880, 1000, 1100, 1200, 1320, 1375, 1500, 1650, 2000, 2200, 2640, 2750, 3000, 3300, 4125, 4400, 5500, 6000, 6600, 8250, 11000, 13200, 16500, 22000, 33000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65985 and 66000. The biggest common factor number is the GCF number.
So the greatest common factor 65985 and 66000 is 15.

Also check out the Least Common Multiple of 65985 and 66000