What is the Greatest Common Factor of 1971 and 1989?

Greatest common factor (GCF) of 1971 and 1989 is 9.

GCF(1971,1989) = 9

We will now calculate the prime factors of 1971 and 1989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1971 and 1989.

How to find the GCF of 1971 and 1989?

We will first find the prime factorization of 1971 and 1989. After we will calculate the factors of 1971 and 1989 and find the biggest common factor number .

Step-1: Prime Factorization of 1971

Prime factors of 1971 are 3, 73. Prime factorization of 1971 in exponential form is:

1971 = 3³ × 73¹

Step-2: Prime Factorization of 1989

Prime factors of 1989 are 3, 13, 17. Prime factorization of 1989 in exponential form is:

1989 = 3² × 13¹ × 17¹

Step-3: Factors of 1971

List of positive integer factors of 1971 that divides 1971 without a remainder.

1, 3, 9, 27, 73, 219, 657

Step-4: Factors of 1989

List of positive integer factors of 1989 that divides 1971 without a remainder.

1, 3, 9, 13, 17, 39, 51, 117, 153, 221, 663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1971 and 1989. The biggest common factor number is the GCF number.
So the greatest common factor 1971 and 1989 is 9.

Also check out the Least Common Multiple of 1971 and 1989