What is the Greatest Common Factor of 17670 and 17685?

Greatest common factor (GCF) of 17670 and 17685 is 15.

GCF(17670,17685) = 15

We will now calculate the prime factors of 17670 and 17685, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17670 and 17685.

How to find the GCF of 17670 and 17685?

We will first find the prime factorization of 17670 and 17685. After we will calculate the factors of 17670 and 17685 and find the biggest common factor number .

Step-1: Prime Factorization of 17670

Prime factors of 17670 are 2, 3, 5, 19, 31. Prime factorization of 17670 in exponential form is:

17670 = 2¹ × 3¹ × 5¹ × 19¹ × 31¹

Step-2: Prime Factorization of 17685

Prime factors of 17685 are 3, 5, 131. Prime factorization of 17685 in exponential form is:

17685 = 3³ × 5¹ × 131¹

Step-3: Factors of 17670

List of positive integer factors of 17670 that divides 17670 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 31, 38, 57, 62, 93, 95, 114, 155, 186, 190, 285, 310, 465, 570, 589, 930, 1178, 1767, 2945, 3534, 5890, 8835

Step-4: Factors of 17685

List of positive integer factors of 17685 that divides 17670 without a remainder.

1, 3, 5, 9, 15, 27, 45, 131, 135, 393, 655, 1179, 1965, 3537, 5895

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17670 and 17685. The biggest common factor number is the GCF number.
So the greatest common factor 17670 and 17685 is 15.

Also check out the Least Common Multiple of 17670 and 17685