What is the Greatest Common Factor of 10971 and 10980?

Greatest common factor (GCF) of 10971 and 10980 is 9.

GCF(10971,10980) = 9

We will now calculate the prime factors of 10971 and 10980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10971 and 10980.

How to find the GCF of 10971 and 10980?

We will first find the prime factorization of 10971 and 10980. After we will calculate the factors of 10971 and 10980 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 10980

Prime factors of 10980 are 2, 3, 5, 61. Prime factorization of 10980 in exponential form is:

10980 = 2² × 3² × 5¹ × 61¹

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 10980

List of positive integer factors of 10980 that divides 10971 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 61, 90, 122, 180, 183, 244, 305, 366, 549, 610, 732, 915, 1098, 1220, 1830, 2196, 2745, 3660, 5490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10971 and 10980. The biggest common factor number is the GCF number.
So the greatest common factor 10971 and 10980 is 9.

Also check out the Least Common Multiple of 10971 and 10980