What is the Greatest Common Factor of 1440 and 1445?

Greatest common factor (GCF) of 1440 and 1445 is 5.

GCF(1440,1445) = 5

We will now calculate the prime factors of 1440 and 1445, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1440 and 1445.

How to find the GCF of 1440 and 1445?

We will first find the prime factorization of 1440 and 1445. After we will calculate the factors of 1440 and 1445 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 1445

Prime factors of 1445 are 5, 17. Prime factorization of 1445 in exponential form is:

1445 = 5¹ × 17²

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 1445

List of positive integer factors of 1445 that divides 1440 without a remainder.

1, 5, 17, 85, 289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1440 and 1445. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1445 is 5.

Also check out the Least Common Multiple of 1440 and 1445