What is the Greatest Common Factor of 20985 and 21000?

Greatest common factor (GCF) of 20985 and 21000 is 15.

GCF(20985,21000) = 15

We will now calculate the prime factors of 20985 and 21000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20985 and 21000.

How to find the GCF of 20985 and 21000?

We will first find the prime factorization of 20985 and 21000. After we will calculate the factors of 20985 and 21000 and find the biggest common factor number .

Step-1: Prime Factorization of 20985

Prime factors of 20985 are 3, 5, 1399. Prime factorization of 20985 in exponential form is:

20985 = 3¹ × 5¹ × 1399¹

Step-2: Prime Factorization of 21000

Prime factors of 21000 are 2, 3, 5, 7. Prime factorization of 21000 in exponential form is:

21000 = 2³ × 3¹ × 5³ × 7¹

Step-3: Factors of 20985

List of positive integer factors of 20985 that divides 20985 without a remainder.

1, 3, 5, 15, 1399, 4197, 6995

Step-4: Factors of 21000

List of positive integer factors of 21000 that divides 20985 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 125, 140, 150, 168, 175, 200, 210, 250, 280, 300, 350, 375, 420, 500, 525, 600, 700, 750, 840, 875, 1000, 1050, 1400, 1500, 1750, 2100, 2625, 3000, 3500, 4200, 5250, 7000, 10500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20985 and 21000. The biggest common factor number is the GCF number.
So the greatest common factor 20985 and 21000 is 15.

Also check out the Least Common Multiple of 20985 and 21000