What is the Greatest Common Factor of 1440 and 1448?

Greatest common factor (GCF) of 1440 and 1448 is 8.

GCF(1440,1448) = 8

We will now calculate the prime factors of 1440 and 1448, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1440 and 1448.

How to find the GCF of 1440 and 1448?

We will first find the prime factorization of 1440 and 1448. After we will calculate the factors of 1440 and 1448 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 1448

Prime factors of 1448 are 2, 181. Prime factorization of 1448 in exponential form is:

1448 = 2³ × 181¹

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 1448

List of positive integer factors of 1448 that divides 1440 without a remainder.

1, 2, 4, 8, 181, 362, 724

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1440 and 1448. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1448 is 8.

Also check out the Least Common Multiple of 1440 and 1448