What is the Greatest Common Factor of 1364 and 1380?

Greatest common factor (GCF) of 1364 and 1380 is 4.

GCF(1364,1380) = 4

We will now calculate the prime factors of 1364 and 1380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1364 and 1380.

How to find the GCF of 1364 and 1380?

We will first find the prime factorization of 1364 and 1380. After we will calculate the factors of 1364 and 1380 and find the biggest common factor number .

Step-1: 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-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 1364

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

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

Step-4: Factors of 1380

List of positive integer factors of 1380 that divides 1364 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 1364 and 1380. The biggest common factor number is the GCF number.
So the greatest common factor 1364 and 1380 is 4.

Also check out the Least Common Multiple of 1364 and 1380