What is the Greatest Common Factor of 1945 and 1950?

Greatest common factor (GCF) of 1945 and 1950 is 5.

GCF(1945,1950) = 5

We will now calculate the prime factors of 1945 and 1950, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1945 and 1950.

How to find the GCF of 1945 and 1950?

We will first find the prime factorization of 1945 and 1950. After we will calculate the factors of 1945 and 1950 and find the biggest common factor number .

Step-1: Prime Factorization of 1945

Prime factors of 1945 are 5, 389. Prime factorization of 1945 in exponential form is:

1945 = 5¹ × 389¹

Step-2: 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-3: Factors of 1945

List of positive integer factors of 1945 that divides 1945 without a remainder.

1, 5, 389

Step-4: Factors of 1950

List of positive integer factors of 1950 that divides 1945 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1945 and 1950. The biggest common factor number is the GCF number.
So the greatest common factor 1945 and 1950 is 5.

Also check out the Least Common Multiple of 1945 and 1950