What is the Greatest Common Factor of 5125 and 5140?

Greatest common factor (GCF) of 5125 and 5140 is 5.

GCF(5125,5140) = 5

We will now calculate the prime factors of 5125 and 5140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5125 and 5140.

How to find the GCF of 5125 and 5140?

We will first find the prime factorization of 5125 and 5140. After we will calculate the factors of 5125 and 5140 and find the biggest common factor number .

Step-1: Prime Factorization of 5125

Prime factors of 5125 are 5, 41. Prime factorization of 5125 in exponential form is:

5125 = 5³ × 41¹

Step-2: Prime Factorization of 5140

Prime factors of 5140 are 2, 5, 257. Prime factorization of 5140 in exponential form is:

5140 = 2² × 5¹ × 257¹

Step-3: Factors of 5125

List of positive integer factors of 5125 that divides 5125 without a remainder.

1, 5, 25, 41, 125, 205, 1025

Step-4: Factors of 5140

List of positive integer factors of 5140 that divides 5125 without a remainder.

1, 2, 4, 5, 10, 20, 257, 514, 1028, 1285, 2570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5125 and 5140. The biggest common factor number is the GCF number.
So the greatest common factor 5125 and 5140 is 5.

Also check out the Least Common Multiple of 5125 and 5140