What is the Greatest Common Factor of 21980 and 21996?

Greatest common factor (GCF) of 21980 and 21996 is 4.

GCF(21980,21996) = 4

We will now calculate the prime factors of 21980 and 21996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21980 and 21996.

How to find the GCF of 21980 and 21996?

We will first find the prime factorization of 21980 and 21996. After we will calculate the factors of 21980 and 21996 and find the biggest common factor number .

Step-1: Prime Factorization of 21980

Prime factors of 21980 are 2, 5, 7, 157. Prime factorization of 21980 in exponential form is:

21980 = 2² × 5¹ × 7¹ × 157¹

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 21980

List of positive integer factors of 21980 that divides 21980 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 157, 314, 628, 785, 1099, 1570, 2198, 3140, 4396, 5495, 10990

Step-4: Factors of 21996

List of positive integer factors of 21996 that divides 21980 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 21980 and 21996. The biggest common factor number is the GCF number.
So the greatest common factor 21980 and 21996 is 4.

Also check out the Least Common Multiple of 21980 and 21996