What is the Greatest Common Factor of 1360 and 1380?

Greatest common factor (GCF) of 1360 and 1380 is 20.

GCF(1360,1380) = 20

We will now calculate the prime factors of 1360 and 1380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1360 and 1380.

How to find the GCF of 1360 and 1380?

We will first find the prime factorization of 1360 and 1380. After we will calculate the factors of 1360 and 1380 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 1380

Prime factors of 1380 are 2, 3, 5, 23. Prime factorization of 1380 in exponential form is:

1380 = 2² × 3¹ × 5¹ × 23¹

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 1380

List of positive integer factors of 1380 that divides 1360 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1360 and 1380. The biggest common factor number is the GCF number.
So the greatest common factor 1360 and 1380 is 20.

Also check out the Least Common Multiple of 1360 and 1380