What is the Greatest Common Factor of 13400 and 13414?

Greatest common factor (GCF) of 13400 and 13414 is 2.

GCF(13400,13414) = 2

We will now calculate the prime factors of 13400 and 13414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13400 and 13414.

How to find the GCF of 13400 and 13414?

We will first find the prime factorization of 13400 and 13414. After we will calculate the factors of 13400 and 13414 and find the biggest common factor number .

Step-1: Prime Factorization of 13400

Prime factors of 13400 are 2, 5, 67. Prime factorization of 13400 in exponential form is:

13400 = 2³ × 5² × 67¹

Step-2: Prime Factorization of 13414

Prime factors of 13414 are 2, 19, 353. Prime factorization of 13414 in exponential form is:

13414 = 2¹ × 19¹ × 353¹

Step-3: Factors of 13400

List of positive integer factors of 13400 that divides 13400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 134, 200, 268, 335, 536, 670, 1340, 1675, 2680, 3350, 6700

Step-4: Factors of 13414

List of positive integer factors of 13414 that divides 13400 without a remainder.

1, 2, 19, 38, 353, 706, 6707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13400 and 13414. The biggest common factor number is the GCF number.
So the greatest common factor 13400 and 13414 is 2.

Also check out the Least Common Multiple of 13400 and 13414