What is the Greatest Common Factor of 3584 and 3598?

Greatest common factor (GCF) of 3584 and 3598 is 14.

GCF(3584,3598) = 14

We will now calculate the prime factors of 3584 and 3598, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3584 and 3598.

How to find the GCF of 3584 and 3598?

We will first find the prime factorization of 3584 and 3598. After we will calculate the factors of 3584 and 3598 and find the biggest common factor number .

Step-1: Prime Factorization of 3584

Prime factors of 3584 are 2, 7. Prime factorization of 3584 in exponential form is:

3584 = 2⁹ × 7¹

Step-2: Prime Factorization of 3598

Prime factors of 3598 are 2, 7, 257. Prime factorization of 3598 in exponential form is:

3598 = 2¹ × 7¹ × 257¹

Step-3: Factors of 3584

List of positive integer factors of 3584 that divides 3584 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792

Step-4: Factors of 3598

List of positive integer factors of 3598 that divides 3584 without a remainder.

1, 2, 7, 14, 257, 514, 1799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3584 and 3598. The biggest common factor number is the GCF number.
So the greatest common factor 3584 and 3598 is 14.

Also check out the Least Common Multiple of 3584 and 3598