What is the Greatest Common Factor of 21975 and 21990?

Greatest common factor (GCF) of 21975 and 21990 is 15.

GCF(21975,21990) = 15

We will now calculate the prime factors of 21975 and 21990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21975 and 21990.

How to find the GCF of 21975 and 21990?

We will first find the prime factorization of 21975 and 21990. After we will calculate the factors of 21975 and 21990 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 21990

Prime factors of 21990 are 2, 3, 5, 733. Prime factorization of 21990 in exponential form is:

21990 = 2¹ × 3¹ × 5¹ × 733¹

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 21990

List of positive integer factors of 21990 that divides 21975 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 733, 1466, 2199, 3665, 4398, 7330, 10995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21975 and 21990. The biggest common factor number is the GCF number.
So the greatest common factor 21975 and 21990 is 15.

Also check out the Least Common Multiple of 21975 and 21990