What is the Greatest Common Factor of 1965 and 1980?

Greatest common factor (GCF) of 1965 and 1980 is 15.

GCF(1965,1980) = 15

We will now calculate the prime factors of 1965 and 1980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1965 and 1980.

How to find the GCF of 1965 and 1980?

We will first find the prime factorization of 1965 and 1980. After we will calculate the factors of 1965 and 1980 and find the biggest common factor number .

Step-1: Prime Factorization of 1965

Prime factors of 1965 are 3, 5, 131. Prime factorization of 1965 in exponential form is:

1965 = 3¹ × 5¹ × 131¹

Step-2: Prime Factorization of 1980

Prime factors of 1980 are 2, 3, 5, 11. Prime factorization of 1980 in exponential form is:

1980 = 2² × 3² × 5¹ × 11¹

Step-3: Factors of 1965

List of positive integer factors of 1965 that divides 1965 without a remainder.

1, 3, 5, 15, 131, 393, 655

Step-4: Factors of 1980

List of positive integer factors of 1980 that divides 1965 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1965 and 1980. The biggest common factor number is the GCF number.
So the greatest common factor 1965 and 1980 is 15.

Also check out the Least Common Multiple of 1965 and 1980