What is the Greatest Common Factor of 1350 and 1370?

Greatest common factor (GCF) of 1350 and 1370 is 10.

GCF(1350,1370) = 10

We will now calculate the prime factors of 1350 and 1370, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1350 and 1370.

How to find the GCF of 1350 and 1370?

We will first find the prime factorization of 1350 and 1370. After we will calculate the factors of 1350 and 1370 and find the biggest common factor number .

Step-1: Prime Factorization of 1350

Prime factors of 1350 are 2, 3, 5. Prime factorization of 1350 in exponential form is:

1350 = 2¹ × 3³ × 5²

Step-2: Prime Factorization of 1370

Prime factors of 1370 are 2, 5, 137. Prime factorization of 1370 in exponential form is:

1370 = 2¹ × 5¹ × 137¹

Step-3: Factors of 1350

List of positive integer factors of 1350 that divides 1350 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675

Step-4: Factors of 1370

List of positive integer factors of 1370 that divides 1350 without a remainder.

1, 2, 5, 10, 137, 274, 685

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1350 and 1370. The biggest common factor number is the GCF number.
So the greatest common factor 1350 and 1370 is 10.

Also check out the Least Common Multiple of 1350 and 1370