What is the Greatest Common Factor of 21998 and 22014?

Greatest common factor (GCF) of 21998 and 22014 is 2.

GCF(21998,22014) = 2

We will now calculate the prime factors of 21998 and 22014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21998 and 22014.

How to find the GCF of 21998 and 22014?

We will first find the prime factorization of 21998 and 22014. After we will calculate the factors of 21998 and 22014 and find the biggest common factor number .

Step-1: Prime Factorization of 21998

Prime factors of 21998 are 2, 17, 647. Prime factorization of 21998 in exponential form is:

21998 = 2¹ × 17¹ × 647¹

Step-2: Prime Factorization of 22014

Prime factors of 22014 are 2, 3, 1223. Prime factorization of 22014 in exponential form is:

22014 = 2¹ × 3² × 1223¹

Step-3: Factors of 21998

List of positive integer factors of 21998 that divides 21998 without a remainder.

1, 2, 17, 34, 647, 1294, 10999

Step-4: Factors of 22014

List of positive integer factors of 22014 that divides 21998 without a remainder.

1, 2, 3, 6, 9, 18, 1223, 2446, 3669, 7338, 11007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21998 and 22014. The biggest common factor number is the GCF number.
So the greatest common factor 21998 and 22014 is 2.

Also check out the Least Common Multiple of 21998 and 22014