What is the Greatest Common Factor of 21960 and 21972?

Greatest common factor (GCF) of 21960 and 21972 is 12.

GCF(21960,21972) = 12

We will now calculate the prime factors of 21960 and 21972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21960 and 21972.

How to find the GCF of 21960 and 21972?

We will first find the prime factorization of 21960 and 21972. After we will calculate the factors of 21960 and 21972 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 21972

Prime factors of 21972 are 2, 3, 1831. Prime factorization of 21972 in exponential form is:

21972 = 2² × 3¹ × 1831¹

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 21972

List of positive integer factors of 21972 that divides 21960 without a remainder.

1, 2, 3, 4, 6, 12, 1831, 3662, 5493, 7324, 10986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21960 and 21972. The biggest common factor number is the GCF number.
So the greatest common factor 21960 and 21972 is 12.

Also check out the Least Common Multiple of 21960 and 21972