What is the Greatest Common Factor of 21978 and 21996?

Greatest common factor (GCF) of 21978 and 21996 is 18.

GCF(21978,21996) = 18

We will now calculate the prime factors of 21978 and 21996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21978 and 21996.

How to find the GCF of 21978 and 21996?

We will first find the prime factorization of 21978 and 21996. After we will calculate the factors of 21978 and 21996 and find the biggest common factor number .

Step-1: Prime Factorization of 21978

Prime factors of 21978 are 2, 3, 11, 37. Prime factorization of 21978 in exponential form is:

21978 = 2¹ × 3³ × 11¹ × 37¹

Step-2: Prime Factorization of 21996

Prime factors of 21996 are 2, 3, 13, 47. Prime factorization of 21996 in exponential form is:

21996 = 2² × 3² × 13¹ × 47¹

Step-3: Factors of 21978

List of positive integer factors of 21978 that divides 21978 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 37, 54, 66, 74, 99, 111, 198, 222, 297, 333, 407, 594, 666, 814, 999, 1221, 1998, 2442, 3663, 7326, 10989

Step-4: Factors of 21996

List of positive integer factors of 21996 that divides 21978 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 47, 52, 78, 94, 117, 141, 156, 188, 234, 282, 423, 468, 564, 611, 846, 1222, 1692, 1833, 2444, 3666, 5499, 7332, 10998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21978 and 21996. The biggest common factor number is the GCF number.
So the greatest common factor 21978 and 21996 is 18.

Also check out the Least Common Multiple of 21978 and 21996