What is the Greatest Common Factor of 17670 and 17680?

Greatest common factor (GCF) of 17670 and 17680 is 10.

GCF(17670,17680) = 10

We will now calculate the prime factors of 17670 and 17680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17670 and 17680.

How to find the GCF of 17670 and 17680?

We will first find the prime factorization of 17670 and 17680. After we will calculate the factors of 17670 and 17680 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 17680

Prime factors of 17680 are 2, 5, 13, 17. Prime factorization of 17680 in exponential form is:

17680 = 2⁴ × 5¹ × 13¹ × 17¹

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 17680

List of positive integer factors of 17680 that divides 17670 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 26, 34, 40, 52, 65, 68, 80, 85, 104, 130, 136, 170, 208, 221, 260, 272, 340, 442, 520, 680, 884, 1040, 1105, 1360, 1768, 2210, 3536, 4420, 8840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17670 and 17680. The biggest common factor number is the GCF number.
So the greatest common factor 17670 and 17680 is 10.

Also check out the Least Common Multiple of 17670 and 17680