What is the Greatest Common Factor of 17584 and 17590?

Greatest common factor (GCF) of 17584 and 17590 is 2.

GCF(17584,17590) = 2

We will now calculate the prime factors of 17584 and 17590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17584 and 17590.

How to find the GCF of 17584 and 17590?

We will first find the prime factorization of 17584 and 17590. After we will calculate the factors of 17584 and 17590 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17590

Prime factors of 17590 are 2, 5, 1759. Prime factorization of 17590 in exponential form is:

17590 = 2¹ × 5¹ × 1759¹

Step-3: Factors of 17584

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

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

Step-4: Factors of 17590

List of positive integer factors of 17590 that divides 17584 without a remainder.

1, 2, 5, 10, 1759, 3518, 8795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17584 and 17590. The biggest common factor number is the GCF number.
So the greatest common factor 17584 and 17590 is 2.

Also check out the Least Common Multiple of 17584 and 17590