What is the Greatest Common Factor of 1965 and 1974?

Greatest common factor (GCF) of 1965 and 1974 is 3.

GCF(1965,1974) = 3

We will now calculate the prime factors of 1965 and 1974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1965 and 1974.

How to find the GCF of 1965 and 1974?

We will first find the prime factorization of 1965 and 1974. After we will calculate the factors of 1965 and 1974 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 1974

Prime factors of 1974 are 2, 3, 7, 47. Prime factorization of 1974 in exponential form is:

1974 = 2¹ × 3¹ × 7¹ × 47¹

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 1974

List of positive integer factors of 1974 that divides 1965 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1965 and 1974. The biggest common factor number is the GCF number.
So the greatest common factor 1965 and 1974 is 3.

Also check out the Least Common Multiple of 1965 and 1974