What is the Greatest Common Factor of 1258 and 1275?

Greatest common factor (GCF) of 1258 and 1275 is 17.

GCF(1258,1275) = 17

We will now calculate the prime factors of 1258 and 1275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1258 and 1275.

How to find the GCF of 1258 and 1275?

We will first find the prime factorization of 1258 and 1275. After we will calculate the factors of 1258 and 1275 and find the biggest common factor number .

Step-1: Prime Factorization of 1258

Prime factors of 1258 are 2, 17, 37. Prime factorization of 1258 in exponential form is:

1258 = 2¹ × 17¹ × 37¹

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 1258

List of positive integer factors of 1258 that divides 1258 without a remainder.

1, 2, 17, 34, 37, 74, 629

Step-4: Factors of 1275

List of positive integer factors of 1275 that divides 1258 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 1258 and 1275. The biggest common factor number is the GCF number.
So the greatest common factor 1258 and 1275 is 17.

Also check out the Least Common Multiple of 1258 and 1275