What is the Greatest Common Factor of 1440 and 1457?

Greatest common factor (GCF) of 1440 and 1457 is 1.

GCF(1440,1457) = 1

We will now calculate the prime factors of 1440 and 1457, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1440 and 1457.

How to find the GCF of 1440 and 1457?

We will first find the prime factorization of 1440 and 1457. After we will calculate the factors of 1440 and 1457 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 1457

Prime factors of 1457 are 31, 47. Prime factorization of 1457 in exponential form is:

1457 = 31¹ × 47¹

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 1457

List of positive integer factors of 1457 that divides 1440 without a remainder.

1, 31, 47

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1440 and 1457. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1457 is 1.

Also check out the Least Common Multiple of 1440 and 1457