What is the Greatest Common Factor of 10574 and 10584?

Greatest common factor (GCF) of 10574 and 10584 is 2.

GCF(10574,10584) = 2

We will now calculate the prime factors of 10574 and 10584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10574 and 10584.

How to find the GCF of 10574 and 10584?

We will first find the prime factorization of 10574 and 10584. After we will calculate the factors of 10574 and 10584 and find the biggest common factor number .

Step-1: Prime Factorization of 10574

Prime factors of 10574 are 2, 17, 311. Prime factorization of 10574 in exponential form is:

10574 = 2¹ × 17¹ × 311¹

Step-2: Prime Factorization of 10584

Prime factors of 10584 are 2, 3, 7. Prime factorization of 10584 in exponential form is:

10584 = 2³ × 3³ × 7²

Step-3: Factors of 10574

List of positive integer factors of 10574 that divides 10574 without a remainder.

1, 2, 17, 34, 311, 622, 5287

Step-4: Factors of 10584

List of positive integer factors of 10584 that divides 10574 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 49, 54, 56, 63, 72, 84, 98, 108, 126, 147, 168, 189, 196, 216, 252, 294, 378, 392, 441, 504, 588, 756, 882, 1176, 1323, 1512, 1764, 2646, 3528, 5292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10574 and 10584. The biggest common factor number is the GCF number.
So the greatest common factor 10574 and 10584 is 2.

Also check out the Least Common Multiple of 10574 and 10584