What is the Greatest Common Factor of 1295 and 1310?

Greatest common factor (GCF) of 1295 and 1310 is 5.

GCF(1295,1310) = 5

We will now calculate the prime factors of 1295 and 1310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1295 and 1310.

How to find the GCF of 1295 and 1310?

We will first find the prime factorization of 1295 and 1310. After we will calculate the factors of 1295 and 1310 and find the biggest common factor number .

Step-1: Prime Factorization of 1295

Prime factors of 1295 are 5, 7, 37. Prime factorization of 1295 in exponential form is:

1295 = 5¹ × 7¹ × 37¹

Step-2: Prime Factorization of 1310

Prime factors of 1310 are 2, 5, 131. Prime factorization of 1310 in exponential form is:

1310 = 2¹ × 5¹ × 131¹

Step-3: Factors of 1295

List of positive integer factors of 1295 that divides 1295 without a remainder.

1, 5, 7, 35, 37, 185, 259

Step-4: Factors of 1310

List of positive integer factors of 1310 that divides 1295 without a remainder.

1, 2, 5, 10, 131, 262, 655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1295 and 1310. The biggest common factor number is the GCF number.
So the greatest common factor 1295 and 1310 is 5.

Also check out the Least Common Multiple of 1295 and 1310