What is the Greatest Common Factor of 13374 and 13380?

Greatest common factor (GCF) of 13374 and 13380 is 6.

GCF(13374,13380) = 6

We will now calculate the prime factors of 13374 and 13380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13374 and 13380.

How to find the GCF of 13374 and 13380?

We will first find the prime factorization of 13374 and 13380. After we will calculate the factors of 13374 and 13380 and find the biggest common factor number .

Step-1: Prime Factorization of 13374

Prime factors of 13374 are 2, 3, 743. Prime factorization of 13374 in exponential form is:

13374 = 2¹ × 3² × 743¹

Step-2: 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-3: Factors of 13374

List of positive integer factors of 13374 that divides 13374 without a remainder.

1, 2, 3, 6, 9, 18, 743, 1486, 2229, 4458, 6687

Step-4: Factors of 13380

List of positive integer factors of 13380 that divides 13374 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13374 and 13380. The biggest common factor number is the GCF number.
So the greatest common factor 13374 and 13380 is 6.

Also check out the Least Common Multiple of 13374 and 13380