What is the Greatest Common Factor of 17651 and 17670?

Greatest common factor (GCF) of 17651 and 17670 is 19.

GCF(17651,17670) = 19

We will now calculate the prime factors of 17651 and 17670, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17651 and 17670.

How to find the GCF of 17651 and 17670?

We will first find the prime factorization of 17651 and 17670. After we will calculate the factors of 17651 and 17670 and find the biggest common factor number .

Step-1: Prime Factorization of 17651

Prime factors of 17651 are 19, 929. Prime factorization of 17651 in exponential form is:

17651 = 19¹ × 929¹

Step-2: 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-3: Factors of 17651

List of positive integer factors of 17651 that divides 17651 without a remainder.

1, 19, 929

Step-4: Factors of 17670

List of positive integer factors of 17670 that divides 17651 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17651 and 17670. The biggest common factor number is the GCF number.
So the greatest common factor 17651 and 17670 is 19.

Also check out the Least Common Multiple of 17651 and 17670