What is the Greatest Common Factor of 21960 and 21975?

Greatest common factor (GCF) of 21960 and 21975 is 15.

GCF(21960,21975) = 15

We will now calculate the prime factors of 21960 and 21975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21960 and 21975.

How to find the GCF of 21960 and 21975?

We will first find the prime factorization of 21960 and 21975. After we will calculate the factors of 21960 and 21975 and find the biggest common factor number .

Step-1: Prime Factorization of 21960

Prime factors of 21960 are 2, 3, 5, 61. Prime factorization of 21960 in exponential form is:

21960 = 2³ × 3² × 5¹ × 61¹

Step-2: 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-3: Factors of 21960

List of positive integer factors of 21960 that divides 21960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980

Step-4: Factors of 21975

List of positive integer factors of 21975 that divides 21960 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21960 and 21975. The biggest common factor number is the GCF number.
So the greatest common factor 21960 and 21975 is 15.

Also check out the Least Common Multiple of 21960 and 21975