What is the Greatest Common Factor of 17666 and 17677?

Greatest common factor (GCF) of 17666 and 17677 is 11.

GCF(17666,17677) = 11

We will now calculate the prime factors of 17666 and 17677, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17666 and 17677.

How to find the GCF of 17666 and 17677?

We will first find the prime factorization of 17666 and 17677. After we will calculate the factors of 17666 and 17677 and find the biggest common factor number .

Step-1: Prime Factorization of 17666

Prime factors of 17666 are 2, 11, 73. Prime factorization of 17666 in exponential form is:

17666 = 2¹ × 11² × 73¹

Step-2: Prime Factorization of 17677

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

17677 = 11¹ × 1607¹

Step-3: Factors of 17666

List of positive integer factors of 17666 that divides 17666 without a remainder.

1, 2, 11, 22, 73, 121, 146, 242, 803, 1606, 8833

Step-4: Factors of 17677

List of positive integer factors of 17677 that divides 17666 without a remainder.

1, 11, 1607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17666 and 17677. The biggest common factor number is the GCF number.
So the greatest common factor 17666 and 17677 is 11.

Also check out the Least Common Multiple of 17666 and 17677