What is the Greatest Common Factor of 1344 and 1360?

Greatest common factor (GCF) of 1344 and 1360 is 16.

GCF(1344,1360) = 16

We will now calculate the prime factors of 1344 and 1360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1344 and 1360.

How to find the GCF of 1344 and 1360?

We will first find the prime factorization of 1344 and 1360. After we will calculate the factors of 1344 and 1360 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 1360

Prime factors of 1360 are 2, 5, 17. Prime factorization of 1360 in exponential form is:

1360 = 2⁴ × 5¹ × 17¹

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 1360

List of positive integer factors of 1360 that divides 1344 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1344 and 1360. The biggest common factor number is the GCF number.
So the greatest common factor 1344 and 1360 is 16.

Also check out the Least Common Multiple of 1344 and 1360