What is the Greatest Common Factor of 1260 and 1275?

Greatest common factor (GCF) of 1260 and 1275 is 15.

GCF(1260,1275) = 15

We will now calculate the prime factors of 1260 and 1275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1260 and 1275.

How to find the GCF of 1260 and 1275?

We will first find the prime factorization of 1260 and 1275. After we will calculate the factors of 1260 and 1275 and find the biggest common factor number .

Step-1: Prime Factorization of 1260

Prime factors of 1260 are 2, 3, 5, 7. Prime factorization of 1260 in exponential form is:

1260 = 2² × 3² × 5¹ × 7¹

Step-2: 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-3: Factors of 1260

List of positive integer factors of 1260 that divides 1260 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630

Step-4: Factors of 1275

List of positive integer factors of 1275 that divides 1260 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1260 and 1275. The biggest common factor number is the GCF number.
So the greatest common factor 1260 and 1275 is 15.

Also check out the Least Common Multiple of 1260 and 1275