What is the Greatest Common Factor of 1275 and 1280?

Greatest common factor (GCF) of 1275 and 1280 is 5.

GCF(1275,1280) = 5

We will now calculate the prime factors of 1275 and 1280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1275 and 1280.

How to find the GCF of 1275 and 1280?

We will first find the prime factorization of 1275 and 1280. After we will calculate the factors of 1275 and 1280 and find the biggest common factor number .

Step-1: Prime Factorization of 1275

Prime factors of 1275 are 3, 5, 17. Prime factorization of 1275 in exponential form is:

1275 = 3¹ × 5² × 17¹

Step-2: Prime Factorization of 1280

Prime factors of 1280 are 2, 5. Prime factorization of 1280 in exponential form is:

1280 = 2⁸ × 5¹

Step-3: Factors of 1275

List of positive integer factors of 1275 that divides 1275 without a remainder.

1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 425

Step-4: Factors of 1280

List of positive integer factors of 1280 that divides 1275 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1275 and 1280. The biggest common factor number is the GCF number.
So the greatest common factor 1275 and 1280 is 5.

Also check out the Least Common Multiple of 1275 and 1280