What is the Greatest Common Factor of 21000 and 21008?

Greatest common factor (GCF) of 21000 and 21008 is 8.

GCF(21000,21008) = 8

We will now calculate the prime factors of 21000 and 21008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21000 and 21008.

How to find the GCF of 21000 and 21008?

We will first find the prime factorization of 21000 and 21008. After we will calculate the factors of 21000 and 21008 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 21008

Prime factors of 21008 are 2, 13, 101. Prime factorization of 21008 in exponential form is:

21008 = 2⁴ × 13¹ × 101¹

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 21008

List of positive integer factors of 21008 that divides 21000 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 101, 104, 202, 208, 404, 808, 1313, 1616, 2626, 5252, 10504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21000 and 21008. The biggest common factor number is the GCF number.
So the greatest common factor 21000 and 21008 is 8.

Also check out the Least Common Multiple of 21000 and 21008