What is the Greatest Common Factor of 21132 and 21147?

Greatest common factor (GCF) of 21132 and 21147 is 3.

GCF(21132,21147) = 3

We will now calculate the prime factors of 21132 and 21147, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21132 and 21147.

How to find the GCF of 21132 and 21147?

We will first find the prime factorization of 21132 and 21147. After we will calculate the factors of 21132 and 21147 and find the biggest common factor number .

Step-1: Prime Factorization of 21132

Prime factors of 21132 are 2, 3, 587. Prime factorization of 21132 in exponential form is:

21132 = 2² × 3² × 587¹

Step-2: Prime Factorization of 21147

Prime factors of 21147 are 3, 7, 19, 53. Prime factorization of 21147 in exponential form is:

21147 = 3¹ × 7¹ × 19¹ × 53¹

Step-3: Factors of 21132

List of positive integer factors of 21132 that divides 21132 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 587, 1174, 1761, 2348, 3522, 5283, 7044, 10566

Step-4: Factors of 21147

List of positive integer factors of 21147 that divides 21132 without a remainder.

1, 3, 7, 19, 21, 53, 57, 133, 159, 371, 399, 1007, 1113, 3021, 7049

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21132 and 21147. The biggest common factor number is the GCF number.
So the greatest common factor 21132 and 21147 is 3.

Also check out the Least Common Multiple of 21132 and 21147