What is the Greatest Common Factor of 17577 and 17584?

Greatest common factor (GCF) of 17577 and 17584 is 7.

GCF(17577,17584) = 7

We will now calculate the prime factors of 17577 and 17584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17577 and 17584.

How to find the GCF of 17577 and 17584?

We will first find the prime factorization of 17577 and 17584. After we will calculate the factors of 17577 and 17584 and find the biggest common factor number .

Step-1: Prime Factorization of 17577

Prime factors of 17577 are 3, 7, 31. Prime factorization of 17577 in exponential form is:

17577 = 3⁴ × 7¹ × 31¹

Step-2: Prime Factorization of 17584

Prime factors of 17584 are 2, 7, 157. Prime factorization of 17584 in exponential form is:

17584 = 2⁴ × 7¹ × 157¹

Step-3: Factors of 17577

List of positive integer factors of 17577 that divides 17577 without a remainder.

1, 3, 7, 9, 21, 27, 31, 63, 81, 93, 189, 217, 279, 567, 651, 837, 1953, 2511, 5859

Step-4: Factors of 17584

List of positive integer factors of 17584 that divides 17577 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 157, 314, 628, 1099, 1256, 2198, 2512, 4396, 8792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17577 and 17584. The biggest common factor number is the GCF number.
So the greatest common factor 17577 and 17584 is 7.

Also check out the Least Common Multiple of 17577 and 17584