What is the Greatest Common Factor of 17677 and 17688?

Greatest common factor (GCF) of 17677 and 17688 is 11.

GCF(17677,17688) = 11

We will now calculate the prime factors of 17677 and 17688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17677 and 17688.

How to find the GCF of 17677 and 17688?

We will first find the prime factorization of 17677 and 17688. After we will calculate the factors of 17677 and 17688 and find the biggest common factor number .

Step-1: Prime Factorization of 17677

Prime factors of 17677 are 11, 1607. Prime factorization of 17677 in exponential form is:

17677 = 11¹ × 1607¹

Step-2: 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-3: Factors of 17677

List of positive integer factors of 17677 that divides 17677 without a remainder.

1, 11, 1607

Step-4: Factors of 17688

List of positive integer factors of 17688 that divides 17677 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17677 and 17688. The biggest common factor number is the GCF number.
So the greatest common factor 17677 and 17688 is 11.

Also check out the Least Common Multiple of 17677 and 17688