What is the Greatest Common Factor of 1989 and 1995?

Greatest common factor (GCF) of 1989 and 1995 is 3.

GCF(1989,1995) = 3

We will now calculate the prime factors of 1989 and 1995, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1989 and 1995.

How to find the GCF of 1989 and 1995?

We will first find the prime factorization of 1989 and 1995. After we will calculate the factors of 1989 and 1995 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1995

Prime factors of 1995 are 3, 5, 7, 19. Prime factorization of 1995 in exponential form is:

1995 = 3¹ × 5¹ × 7¹ × 19¹

Step-3: Factors of 1989

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

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

Step-4: Factors of 1995

List of positive integer factors of 1995 that divides 1989 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1989 and 1995. The biggest common factor number is the GCF number.
So the greatest common factor 1989 and 1995 is 3.

Also check out the Least Common Multiple of 1989 and 1995