What is the Greatest Common Factor of 36567 and 36584?

Greatest common factor (GCF) of 36567 and 36584 is 17.

GCF(36567,36584) = 17

We will now calculate the prime factors of 36567 and 36584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36567 and 36584.

How to find the GCF of 36567 and 36584?

We will first find the prime factorization of 36567 and 36584. After we will calculate the factors of 36567 and 36584 and find the biggest common factor number .

Step-1: Prime Factorization of 36567

Prime factors of 36567 are 3, 17, 239. Prime factorization of 36567 in exponential form is:

36567 = 3² × 17¹ × 239¹

Step-2: Prime Factorization of 36584

Prime factors of 36584 are 2, 17, 269. Prime factorization of 36584 in exponential form is:

36584 = 2³ × 17¹ × 269¹

Step-3: Factors of 36567

List of positive integer factors of 36567 that divides 36567 without a remainder.

1, 3, 9, 17, 51, 153, 239, 717, 2151, 4063, 12189

Step-4: Factors of 36584

List of positive integer factors of 36584 that divides 36567 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 269, 538, 1076, 2152, 4573, 9146, 18292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36567 and 36584. The biggest common factor number is the GCF number.
So the greatest common factor 36567 and 36584 is 17.

Also check out the Least Common Multiple of 36567 and 36584