What is the Greatest Common Factor of 21969 and 21978?

Greatest common factor (GCF) of 21969 and 21978 is 9.

GCF(21969,21978) = 9

We will now calculate the prime factors of 21969 and 21978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21969 and 21978.

How to find the GCF of 21969 and 21978?

We will first find the prime factorization of 21969 and 21978. After we will calculate the factors of 21969 and 21978 and find the biggest common factor number .

Step-1: Prime Factorization of 21969

Prime factors of 21969 are 3, 2441. Prime factorization of 21969 in exponential form is:

21969 = 3² × 2441¹

Step-2: 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-3: Factors of 21969

List of positive integer factors of 21969 that divides 21969 without a remainder.

1, 3, 9, 2441, 7323

Step-4: Factors of 21978

List of positive integer factors of 21978 that divides 21969 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21969 and 21978. The biggest common factor number is the GCF number.
So the greatest common factor 21969 and 21978 is 9.

Also check out the Least Common Multiple of 21969 and 21978