What is the Greatest Common Factor of 1440 and 1444?

Greatest common factor (GCF) of 1440 and 1444 is 4.

GCF(1440,1444) = 4

We will now calculate the prime factors of 1440 and 1444, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1440 and 1444.

How to find the GCF of 1440 and 1444?

We will first find the prime factorization of 1440 and 1444. After we will calculate the factors of 1440 and 1444 and find the biggest common factor number .

Step-1: Prime Factorization of 1440

Prime factors of 1440 are 2, 3, 5. Prime factorization of 1440 in exponential form is:

1440 = 2⁵ × 3² × 5¹

Step-2: Prime Factorization of 1444

Prime factors of 1444 are 2, 19. Prime factorization of 1444 in exponential form is:

1444 = 2² × 19²

Step-3: Factors of 1440

List of positive integer factors of 1440 that divides 1440 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720

Step-4: Factors of 1444

List of positive integer factors of 1444 that divides 1440 without a remainder.

1, 2, 4, 19, 38, 76, 361, 722

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1440 and 1444. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1444 is 4.

Also check out the Least Common Multiple of 1440 and 1444