What is the Greatest Common Factor of 17688 and 17705?

Greatest common factor (GCF) of 17688 and 17705 is 1.

GCF(17688,17705) = 1

We will now calculate the prime factors of 17688 and 17705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17688 and 17705.

How to find the GCF of 17688 and 17705?

We will first find the prime factorization of 17688 and 17705. After we will calculate the factors of 17688 and 17705 and find the biggest common factor number .

Step-1: Prime Factorization of 17688

Prime factors of 17688 are 2, 3, 11, 67. Prime factorization of 17688 in exponential form is:

17688 = 2³ × 3¹ × 11¹ × 67¹

Step-2: Prime Factorization of 17705

Prime factors of 17705 are 5, 3541. Prime factorization of 17705 in exponential form is:

17705 = 5¹ × 3541¹

Step-3: Factors of 17688

List of positive integer factors of 17688 that divides 17688 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 67, 88, 132, 134, 201, 264, 268, 402, 536, 737, 804, 1474, 1608, 2211, 2948, 4422, 5896, 8844

Step-4: Factors of 17705

List of positive integer factors of 17705 that divides 17688 without a remainder.

1, 5, 3541

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17688 and 17705. The biggest common factor number is the GCF number.
So the greatest common factor 17688 and 17705 is 1.

Also check out the Least Common Multiple of 17688 and 17705