What is the Greatest Common Factor of 13380 and 13400?

Greatest common factor (GCF) of 13380 and 13400 is 20.

GCF(13380,13400) = 20

We will now calculate the prime factors of 13380 and 13400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13380 and 13400.

How to find the GCF of 13380 and 13400?

We will first find the prime factorization of 13380 and 13400. After we will calculate the factors of 13380 and 13400 and find the biggest common factor number .

Step-1: Prime Factorization of 13380

Prime factors of 13380 are 2, 3, 5, 223. Prime factorization of 13380 in exponential form is:

13380 = 2² × 3¹ × 5¹ × 223¹

Step-2: 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-3: Factors of 13380

List of positive integer factors of 13380 that divides 13380 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 223, 446, 669, 892, 1115, 1338, 2230, 2676, 3345, 4460, 6690

Step-4: Factors of 13400

List of positive integer factors of 13400 that divides 13380 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13380 and 13400. The biggest common factor number is the GCF number.
So the greatest common factor 13380 and 13400 is 20.

Also check out the Least Common Multiple of 13380 and 13400