What is the Greatest Common Factor of 21986 and 22000?

Greatest common factor (GCF) of 21986 and 22000 is 2.

GCF(21986,22000) = 2

We will now calculate the prime factors of 21986 and 22000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21986 and 22000.

How to find the GCF of 21986 and 22000?

We will first find the prime factorization of 21986 and 22000. After we will calculate the factors of 21986 and 22000 and find the biggest common factor number .

Step-1: Prime Factorization of 21986

Prime factors of 21986 are 2, 10993. Prime factorization of 21986 in exponential form is:

21986 = 2¹ × 10993¹

Step-2: Prime Factorization of 22000

Prime factors of 22000 are 2, 5, 11. Prime factorization of 22000 in exponential form is:

22000 = 2⁴ × 5³ × 11¹

Step-3: Factors of 21986

List of positive integer factors of 21986 that divides 21986 without a remainder.

1, 2, 10993

Step-4: Factors of 22000

List of positive integer factors of 22000 that divides 21986 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 125, 176, 200, 220, 250, 275, 400, 440, 500, 550, 880, 1000, 1100, 1375, 2000, 2200, 2750, 4400, 5500, 11000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21986 and 22000. The biggest common factor number is the GCF number.
So the greatest common factor 21986 and 22000 is 2.

Also check out the Least Common Multiple of 21986 and 22000