What is the Greatest Common Factor of 5140 and 5160?

Greatest common factor (GCF) of 5140 and 5160 is 20.

GCF(5140,5160) = 20

We will now calculate the prime factors of 5140 and 5160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5140 and 5160.

How to find the GCF of 5140 and 5160?

We will first find the prime factorization of 5140 and 5160. After we will calculate the factors of 5140 and 5160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5160

Prime factors of 5160 are 2, 3, 5, 43. Prime factorization of 5160 in exponential form is:

5160 = 2³ × 3¹ × 5¹ × 43¹

Step-3: Factors of 5140

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

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

Step-4: Factors of 5160

List of positive integer factors of 5160 that divides 5140 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 43, 60, 86, 120, 129, 172, 215, 258, 344, 430, 516, 645, 860, 1032, 1290, 1720, 2580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5140 and 5160. The biggest common factor number is the GCF number.
So the greatest common factor 5140 and 5160 is 20.

Also check out the Least Common Multiple of 5140 and 5160