What is the Greatest Common Factor of 1440 and 1456?

Greatest common factor (GCF) of 1440 and 1456 is 16.

GCF(1440,1456) = 16

We will now calculate the prime factors of 1440 and 1456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1440 and 1456.

How to find the GCF of 1440 and 1456?

We will first find the prime factorization of 1440 and 1456. After we will calculate the factors of 1440 and 1456 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 1456

Prime factors of 1456 are 2, 7, 13. Prime factorization of 1456 in exponential form is:

1456 = 2⁴ × 7¹ × 13¹

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 1456

List of positive integer factors of 1456 that divides 1440 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1440 and 1456. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1456 is 16.

Also check out the Least Common Multiple of 1440 and 1456