What is the Greatest Common Factor of 67250 and 67270?

Greatest common factor (GCF) of 67250 and 67270 is 10.

GCF(67250,67270) = 10

We will now calculate the prime factors of 67250 and 67270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67250 and 67270.

How to find the GCF of 67250 and 67270?

We will first find the prime factorization of 67250 and 67270. After we will calculate the factors of 67250 and 67270 and find the biggest common factor number .

Step-1: Prime Factorization of 67250

Prime factors of 67250 are 2, 5, 269. Prime factorization of 67250 in exponential form is:

67250 = 2¹ × 5³ × 269¹

Step-2: Prime Factorization of 67270

Prime factors of 67270 are 2, 5, 7, 31. Prime factorization of 67270 in exponential form is:

67270 = 2¹ × 5¹ × 7¹ × 31²

Step-3: Factors of 67250

List of positive integer factors of 67250 that divides 67250 without a remainder.

1, 2, 5, 10, 25, 50, 125, 250, 269, 538, 1345, 2690, 6725, 13450, 33625

Step-4: Factors of 67270

List of positive integer factors of 67270 that divides 67250 without a remainder.

1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 961, 1085, 1922, 2170, 4805, 6727, 9610, 13454, 33635

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67250 and 67270. The biggest common factor number is the GCF number.
So the greatest common factor 67250 and 67270 is 10.

Also check out the Least Common Multiple of 67250 and 67270