What is the Greatest Common Factor of 1967 and 1974?

Greatest common factor (GCF) of 1967 and 1974 is 7.

GCF(1967,1974) = 7

We will now calculate the prime factors of 1967 and 1974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1967 and 1974.

How to find the GCF of 1967 and 1974?

We will first find the prime factorization of 1967 and 1974. After we will calculate the factors of 1967 and 1974 and find the biggest common factor number .

Step-1: Prime Factorization of 1967

Prime factors of 1967 are 7, 281. Prime factorization of 1967 in exponential form is:

1967 = 7¹ × 281¹

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 1967

List of positive integer factors of 1967 that divides 1967 without a remainder.

1, 7, 281

Step-4: Factors of 1974

List of positive integer factors of 1974 that divides 1967 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 1967 and 1974. The biggest common factor number is the GCF number.
So the greatest common factor 1967 and 1974 is 7.

Also check out the Least Common Multiple of 1967 and 1974