What is the Greatest Common Factor of 14125 and 14140?

Greatest common factor (GCF) of 14125 and 14140 is 5.

GCF(14125,14140) = 5

We will now calculate the prime factors of 14125 and 14140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14125 and 14140.

How to find the GCF of 14125 and 14140?

We will first find the prime factorization of 14125 and 14140. After we will calculate the factors of 14125 and 14140 and find the biggest common factor number .

Step-1: Prime Factorization of 14125

Prime factors of 14125 are 5, 113. Prime factorization of 14125 in exponential form is:

14125 = 5³ × 113¹

Step-2: Prime Factorization of 14140

Prime factors of 14140 are 2, 5, 7, 101. Prime factorization of 14140 in exponential form is:

14140 = 2² × 5¹ × 7¹ × 101¹

Step-3: Factors of 14125

List of positive integer factors of 14125 that divides 14125 without a remainder.

1, 5, 25, 113, 125, 565, 2825

Step-4: Factors of 14140

List of positive integer factors of 14140 that divides 14125 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 101, 140, 202, 404, 505, 707, 1010, 1414, 2020, 2828, 3535, 7070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14125 and 14140. The biggest common factor number is the GCF number.
So the greatest common factor 14125 and 14140 is 5.

Also check out the Least Common Multiple of 14125 and 14140