What is the Greatest Common Factor of 1250 and 1265?

Greatest common factor (GCF) of 1250 and 1265 is 5.

GCF(1250,1265) = 5

We will now calculate the prime factors of 1250 and 1265, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1250 and 1265.

How to find the GCF of 1250 and 1265?

We will first find the prime factorization of 1250 and 1265. After we will calculate the factors of 1250 and 1265 and find the biggest common factor number .

Step-1: Prime Factorization of 1250

Prime factors of 1250 are 2, 5. Prime factorization of 1250 in exponential form is:

1250 = 2¹ × 5⁴

Step-2: Prime Factorization of 1265

Prime factors of 1265 are 5, 11, 23. Prime factorization of 1265 in exponential form is:

1265 = 5¹ × 11¹ × 23¹

Step-3: Factors of 1250

List of positive integer factors of 1250 that divides 1250 without a remainder.

1, 2, 5, 10, 25, 50, 125, 250, 625

Step-4: Factors of 1265

List of positive integer factors of 1265 that divides 1250 without a remainder.

1, 5, 11, 23, 55, 115, 253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1250 and 1265. The biggest common factor number is the GCF number.
So the greatest common factor 1250 and 1265 is 5.

Also check out the Least Common Multiple of 1250 and 1265