What is the Greatest Common Factor of 62985 and 63000?

Greatest common factor (GCF) of 62985 and 63000 is 15.

GCF(62985,63000) = 15

We will now calculate the prime factors of 62985 and 63000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 62985 and 63000.

How to find the GCF of 62985 and 63000?

We will first find the prime factorization of 62985 and 63000. After we will calculate the factors of 62985 and 63000 and find the biggest common factor number .

Step-1: Prime Factorization of 62985

Prime factors of 62985 are 3, 5, 13, 17, 19. Prime factorization of 62985 in exponential form is:

62985 = 3¹ × 5¹ × 13¹ × 17¹ × 19¹

Step-2: Prime Factorization of 63000

Prime factors of 63000 are 2, 3, 5, 7. Prime factorization of 63000 in exponential form is:

63000 = 2³ × 3² × 5³ × 7¹

Step-3: Factors of 62985

List of positive integer factors of 62985 that divides 62985 without a remainder.

1, 3, 5, 13, 15, 17, 19, 39, 51, 57, 65, 85, 95, 195, 221, 247, 255, 285, 323, 663, 741, 969, 1105, 1235, 1615, 3315, 3705, 4199, 4845, 12597, 20995

Step-4: Factors of 63000

List of positive integer factors of 63000 that divides 62985 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 50, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 120, 125, 126, 140, 150, 168, 175, 180, 200, 210, 225, 250, 252, 280, 300, 315, 350, 360, 375, 420, 450, 500, 504, 525, 600, 630, 700, 750, 840, 875, 900, 1000, 1050, 1125, 1260, 1400, 1500, 1575, 1750, 1800, 2100, 2250, 2520, 2625, 3000, 3150, 3500, 4200, 4500, 5250, 6300, 7000, 7875, 9000, 10500, 12600, 15750, 21000, 31500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 62985 and 63000. The biggest common factor number is the GCF number.
So the greatest common factor 62985 and 63000 is 15.

Also check out the Least Common Multiple of 62985 and 63000