What is the Greatest Common Factor of 10971 and 10986?

Greatest common factor (GCF) of 10971 and 10986 is 3.

GCF(10971,10986) = 3

We will now calculate the prime factors of 10971 and 10986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10971 and 10986.

How to find the GCF of 10971 and 10986?

We will first find the prime factorization of 10971 and 10986. After we will calculate the factors of 10971 and 10986 and find the biggest common factor number .

Step-1: Prime Factorization of 10971

Prime factors of 10971 are 3, 23, 53. Prime factorization of 10971 in exponential form is:

10971 = 3² × 23¹ × 53¹

Step-2: Prime Factorization of 10986

Prime factors of 10986 are 2, 3, 1831. Prime factorization of 10986 in exponential form is:

10986 = 2¹ × 3¹ × 1831¹

Step-3: Factors of 10971

List of positive integer factors of 10971 that divides 10971 without a remainder.

1, 3, 9, 23, 53, 69, 159, 207, 477, 1219, 3657

Step-4: Factors of 10986

List of positive integer factors of 10986 that divides 10971 without a remainder.

1, 2, 3, 6, 1831, 3662, 5493

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10971 and 10986. The biggest common factor number is the GCF number.
So the greatest common factor 10971 and 10986 is 3.

Also check out the Least Common Multiple of 10971 and 10986