What is the Greatest Common Factor of 1950 and 1960?

Greatest common factor (GCF) of 1950 and 1960 is 10.

GCF(1950,1960) = 10

We will now calculate the prime factors of 1950 and 1960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1950 and 1960.

How to find the GCF of 1950 and 1960?

We will first find the prime factorization of 1950 and 1960. After we will calculate the factors of 1950 and 1960 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 1960

Prime factors of 1960 are 2, 5, 7. Prime factorization of 1960 in exponential form is:

1960 = 2³ × 5¹ × 7²

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 1960

List of positive integer factors of 1960 that divides 1950 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1950 and 1960. The biggest common factor number is the GCF number.
So the greatest common factor 1950 and 1960 is 10.

Also check out the Least Common Multiple of 1950 and 1960