What is the Greatest Common Factor of 21975 and 21980?

Greatest common factor (GCF) of 21975 and 21980 is 5.

GCF(21975,21980) = 5

We will now calculate the prime factors of 21975 and 21980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21975 and 21980.

How to find the GCF of 21975 and 21980?

We will first find the prime factorization of 21975 and 21980. After we will calculate the factors of 21975 and 21980 and find the biggest common factor number .

Step-1: Prime Factorization of 21975

Prime factors of 21975 are 3, 5, 293. Prime factorization of 21975 in exponential form is:

21975 = 3¹ × 5² × 293¹

Step-2: 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-3: Factors of 21975

List of positive integer factors of 21975 that divides 21975 without a remainder.

1, 3, 5, 15, 25, 75, 293, 879, 1465, 4395, 7325

Step-4: Factors of 21980

List of positive integer factors of 21980 that divides 21975 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21975 and 21980. The biggest common factor number is the GCF number.
So the greatest common factor 21975 and 21980 is 5.

Also check out the Least Common Multiple of 21975 and 21980