What is the Greatest Common Factor of 1940 and 1954?

Greatest common factor (GCF) of 1940 and 1954 is 2.

GCF(1940,1954) = 2

We will now calculate the prime factors of 1940 and 1954, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1940 and 1954.

How to find the GCF of 1940 and 1954?

We will first find the prime factorization of 1940 and 1954. After we will calculate the factors of 1940 and 1954 and find the biggest common factor number .

Step-1: Prime Factorization of 1940

Prime factors of 1940 are 2, 5, 97. Prime factorization of 1940 in exponential form is:

1940 = 2² × 5¹ × 97¹

Step-2: Prime Factorization of 1954

Prime factors of 1954 are 2, 977. Prime factorization of 1954 in exponential form is:

1954 = 2¹ × 977¹

Step-3: Factors of 1940

List of positive integer factors of 1940 that divides 1940 without a remainder.

1, 2, 4, 5, 10, 20, 97, 194, 388, 485, 970

Step-4: Factors of 1954

List of positive integer factors of 1954 that divides 1940 without a remainder.

1, 2, 977

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1940 and 1954. The biggest common factor number is the GCF number.
So the greatest common factor 1940 and 1954 is 2.

Also check out the Least Common Multiple of 1940 and 1954