What is the Greatest Common Factor of 19960 and 19975?

Greatest common factor (GCF) of 19960 and 19975 is 5.

GCF(19960,19975) = 5

We will now calculate the prime factors of 19960 and 19975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19960 and 19975.

How to find the GCF of 19960 and 19975?

We will first find the prime factorization of 19960 and 19975. After we will calculate the factors of 19960 and 19975 and find the biggest common factor number .

Step-1: Prime Factorization of 19960

Prime factors of 19960 are 2, 5, 499. Prime factorization of 19960 in exponential form is:

19960 = 2³ × 5¹ × 499¹

Step-2: Prime Factorization of 19975

Prime factors of 19975 are 5, 17, 47. Prime factorization of 19975 in exponential form is:

19975 = 5² × 17¹ × 47¹

Step-3: Factors of 19960

List of positive integer factors of 19960 that divides 19960 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 499, 998, 1996, 2495, 3992, 4990, 9980

Step-4: Factors of 19975

List of positive integer factors of 19975 that divides 19960 without a remainder.

1, 5, 17, 25, 47, 85, 235, 425, 799, 1175, 3995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19960 and 19975. The biggest common factor number is the GCF number.
So the greatest common factor 19960 and 19975 is 5.

Also check out the Least Common Multiple of 19960 and 19975