What is the Greatest Common Factor of 21000 and 21014?

Greatest common factor (GCF) of 21000 and 21014 is 14.

GCF(21000,21014) = 14

We will now calculate the prime factors of 21000 and 21014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21000 and 21014.

How to find the GCF of 21000 and 21014?

We will first find the prime factorization of 21000 and 21014. After we will calculate the factors of 21000 and 21014 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21014

Prime factors of 21014 are 2, 7, 19, 79. Prime factorization of 21014 in exponential form is:

21014 = 2¹ × 7¹ × 19¹ × 79¹

Step-3: Factors of 21000

List of positive integer factors of 21000 that divides 21000 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

Step-4: Factors of 21014

List of positive integer factors of 21014 that divides 21000 without a remainder.

1, 2, 7, 14, 19, 38, 79, 133, 158, 266, 553, 1106, 1501, 3002, 10507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21000 and 21014. The biggest common factor number is the GCF number.
So the greatest common factor 21000 and 21014 is 14.

Also check out the Least Common Multiple of 21000 and 21014