What is the Greatest Common Factor of 1950 and 1970?

Greatest common factor (GCF) of 1950 and 1970 is 10.

GCF(1950,1970) = 10

We will now calculate the prime factors of 1950 and 1970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1950 and 1970.

How to find the GCF of 1950 and 1970?

We will first find the prime factorization of 1950 and 1970. After we will calculate the factors of 1950 and 1970 and find the biggest common factor number .

Step-1: Prime Factorization of 1950

Prime factors of 1950 are 2, 3, 5, 13. Prime factorization of 1950 in exponential form is:

1950 = 2¹ × 3¹ × 5² × 13¹

Step-2: Prime Factorization of 1970

Prime factors of 1970 are 2, 5, 197. Prime factorization of 1970 in exponential form is:

1970 = 2¹ × 5¹ × 197¹

Step-3: Factors of 1950

List of positive integer factors of 1950 that divides 1950 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975

Step-4: Factors of 1970

List of positive integer factors of 1970 that divides 1950 without a remainder.

1, 2, 5, 10, 197, 394, 985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1950 and 1970. The biggest common factor number is the GCF number.
So the greatest common factor 1950 and 1970 is 10.

Also check out the Least Common Multiple of 1950 and 1970