What is the Greatest Common Factor of 1250 and 1270?

Greatest common factor (GCF) of 1250 and 1270 is 10.

GCF(1250,1270) = 10

We will now calculate the prime factors of 1250 and 1270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1250 and 1270.

How to find the GCF of 1250 and 1270?

We will first find the prime factorization of 1250 and 1270. After we will calculate the factors of 1250 and 1270 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 1270

Prime factors of 1270 are 2, 5, 127. Prime factorization of 1270 in exponential form is:

1270 = 2¹ × 5¹ × 127¹

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 1270

List of positive integer factors of 1270 that divides 1250 without a remainder.

1, 2, 5, 10, 127, 254, 635

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1250 and 1270. The biggest common factor number is the GCF number.
So the greatest common factor 1250 and 1270 is 10.

Also check out the Least Common Multiple of 1250 and 1270