What is the Greatest Common Factor of 1250 and 1260?

Greatest common factor (GCF) of 1250 and 1260 is 10.

GCF(1250,1260) = 10

We will now calculate the prime factors of 1250 and 1260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1250 and 1260.

How to find the GCF of 1250 and 1260?

We will first find the prime factorization of 1250 and 1260. After we will calculate the factors of 1250 and 1260 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 1260

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

1260 = 2² × 3² × 5¹ × 7¹

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 1260

List of positive integer factors of 1260 that divides 1250 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1250 and 1260. The biggest common factor number is the GCF number.
So the greatest common factor 1250 and 1260 is 10.

Also check out the Least Common Multiple of 1250 and 1260