What is the Greatest Common Factor of 1344 and 1364?

Greatest common factor (GCF) of 1344 and 1364 is 4.

GCF(1344,1364) = 4

We will now calculate the prime factors of 1344 and 1364, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1344 and 1364.

How to find the GCF of 1344 and 1364?

We will first find the prime factorization of 1344 and 1364. After we will calculate the factors of 1344 and 1364 and find the biggest common factor number .

Step-1: Prime Factorization of 1344

Prime factors of 1344 are 2, 3, 7. Prime factorization of 1344 in exponential form is:

1344 = 2⁶ × 3¹ × 7¹

Step-2: Prime Factorization of 1364

Prime factors of 1364 are 2, 11, 31. Prime factorization of 1364 in exponential form is:

1364 = 2² × 11¹ × 31¹

Step-3: Factors of 1344

List of positive integer factors of 1344 that divides 1344 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 168, 192, 224, 336, 448, 672

Step-4: Factors of 1364

List of positive integer factors of 1364 that divides 1344 without a remainder.

1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1344 and 1364. The biggest common factor number is the GCF number.
So the greatest common factor 1344 and 1364 is 4.

Also check out the Least Common Multiple of 1344 and 1364