What is the Greatest Common Factor of 1425 and 1440?

Greatest common factor (GCF) of 1425 and 1440 is 15.

GCF(1425,1440) = 15

We will now calculate the prime factors of 1425 and 1440, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1425 and 1440.

How to find the GCF of 1425 and 1440?

We will first find the prime factorization of 1425 and 1440. After we will calculate the factors of 1425 and 1440 and find the biggest common factor number .

Step-1: Prime Factorization of 1425

Prime factors of 1425 are 3, 5, 19. Prime factorization of 1425 in exponential form is:

1425 = 3¹ × 5² × 19¹

Step-2: 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-3: Factors of 1425

List of positive integer factors of 1425 that divides 1425 without a remainder.

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475

Step-4: Factors of 1440

List of positive integer factors of 1440 that divides 1425 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1425 and 1440. The biggest common factor number is the GCF number.
So the greatest common factor 1425 and 1440 is 15.

Also check out the Least Common Multiple of 1425 and 1440