What is the Greatest Common Factor of 1300 and 1319?

Greatest common factor (GCF) of 1300 and 1319 is 1.

GCF(1300,1319) = 1

We will now calculate the prime factors of 1300 and 1319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1300 and 1319.

How to find the GCF of 1300 and 1319?

We will first find the prime factorization of 1300 and 1319. After we will calculate the factors of 1300 and 1319 and find the biggest common factor number .

Step-1: Prime Factorization of 1300

Prime factors of 1300 are 2, 5, 13. Prime factorization of 1300 in exponential form is:

1300 = 2² × 5² × 13¹

Step-2: Prime Factorization of 1319

Prime factors of 1319 are 1319. Prime factorization of 1319 in exponential form is:

1319 = 1319¹

Step-3: Factors of 1300

List of positive integer factors of 1300 that divides 1300 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650

Step-4: Factors of 1319

List of positive integer factors of 1319 that divides 1300 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1300 and 1319. The biggest common factor number is the GCF number.
So the greatest common factor 1300 and 1319 is 1.

Also check out the Least Common Multiple of 1300 and 1319