What is the Greatest Common Factor of 21974 and 21994?

Greatest common factor (GCF) of 21974 and 21994 is 2.

GCF(21974,21994) = 2

We will now calculate the prime factors of 21974 and 21994, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21974 and 21994.

How to find the GCF of 21974 and 21994?

We will first find the prime factorization of 21974 and 21994. After we will calculate the factors of 21974 and 21994 and find the biggest common factor number .

Step-1: Prime Factorization of 21974

Prime factors of 21974 are 2, 10987. Prime factorization of 21974 in exponential form is:

21974 = 2¹ × 10987¹

Step-2: Prime Factorization of 21994

Prime factors of 21994 are 2, 7, 1571. Prime factorization of 21994 in exponential form is:

21994 = 2¹ × 7¹ × 1571¹

Step-3: Factors of 21974

List of positive integer factors of 21974 that divides 21974 without a remainder.

1, 2, 10987

Step-4: Factors of 21994

List of positive integer factors of 21994 that divides 21974 without a remainder.

1, 2, 7, 14, 1571, 3142, 10997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21974 and 21994. The biggest common factor number is the GCF number.
So the greatest common factor 21974 and 21994 is 2.

Also check out the Least Common Multiple of 21974 and 21994