What is the Greatest Common Factor of 1360 and 1378?

Greatest common factor (GCF) of 1360 and 1378 is 2.

GCF(1360,1378) = 2

We will now calculate the prime factors of 1360 and 1378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1360 and 1378.

How to find the GCF of 1360 and 1378?

We will first find the prime factorization of 1360 and 1378. After we will calculate the factors of 1360 and 1378 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1378

Prime factors of 1378 are 2, 13, 53. Prime factorization of 1378 in exponential form is:

1378 = 2¹ × 13¹ × 53¹

Step-3: Factors of 1360

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

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

Step-4: Factors of 1378

List of positive integer factors of 1378 that divides 1360 without a remainder.

1, 2, 13, 26, 53, 106, 689

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1360 and 1378. The biggest common factor number is the GCF number.
So the greatest common factor 1360 and 1378 is 2.

Also check out the Least Common Multiple of 1360 and 1378