What is the Greatest Common Factor of 17584 and 17598?

Greatest common factor (GCF) of 17584 and 17598 is 14.

GCF(17584,17598) = 14

We will now calculate the prime factors of 17584 and 17598, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17584 and 17598.

How to find the GCF of 17584 and 17598?

We will first find the prime factorization of 17584 and 17598. After we will calculate the factors of 17584 and 17598 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 17598

Prime factors of 17598 are 2, 3, 7, 419. Prime factorization of 17598 in exponential form is:

17598 = 2¹ × 3¹ × 7¹ × 419¹

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 17598

List of positive integer factors of 17598 that divides 17584 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 419, 838, 1257, 2514, 2933, 5866, 8799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17584 and 17598. The biggest common factor number is the GCF number.
So the greatest common factor 17584 and 17598 is 14.

Also check out the Least Common Multiple of 17584 and 17598