What is the Greatest Common Factor of 13960 and 13975?

Greatest common factor (GCF) of 13960 and 13975 is 5.

GCF(13960,13975) = 5

We will now calculate the prime factors of 13960 and 13975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13960 and 13975.

How to find the GCF of 13960 and 13975?

We will first find the prime factorization of 13960 and 13975. After we will calculate the factors of 13960 and 13975 and find the biggest common factor number .

Step-1: Prime Factorization of 13960

Prime factors of 13960 are 2, 5, 349. Prime factorization of 13960 in exponential form is:

13960 = 2³ × 5¹ × 349¹

Step-2: Prime Factorization of 13975

Prime factors of 13975 are 5, 13, 43. Prime factorization of 13975 in exponential form is:

13975 = 5² × 13¹ × 43¹

Step-3: Factors of 13960

List of positive integer factors of 13960 that divides 13960 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 349, 698, 1396, 1745, 2792, 3490, 6980

Step-4: Factors of 13975

List of positive integer factors of 13975 that divides 13960 without a remainder.

1, 5, 13, 25, 43, 65, 215, 325, 559, 1075, 2795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13960 and 13975. The biggest common factor number is the GCF number.
So the greatest common factor 13960 and 13975 is 5.

Also check out the Least Common Multiple of 13960 and 13975