What is the Greatest Common Factor of 34099 and 34112?

Greatest common factor (GCF) of 34099 and 34112 is 13.

GCF(34099,34112) = 13

We will now calculate the prime factors of 34099 and 34112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34099 and 34112.

How to find the GCF of 34099 and 34112?

We will first find the prime factorization of 34099 and 34112. After we will calculate the factors of 34099 and 34112 and find the biggest common factor number .

Step-1: Prime Factorization of 34099

Prime factors of 34099 are 13, 43, 61. Prime factorization of 34099 in exponential form is:

34099 = 13¹ × 43¹ × 61¹

Step-2: Prime Factorization of 34112

Prime factors of 34112 are 2, 13, 41. Prime factorization of 34112 in exponential form is:

34112 = 2⁶ × 13¹ × 41¹

Step-3: Factors of 34099

List of positive integer factors of 34099 that divides 34099 without a remainder.

1, 13, 43, 61, 559, 793, 2623

Step-4: Factors of 34112

List of positive integer factors of 34112 that divides 34099 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 41, 52, 64, 82, 104, 164, 208, 328, 416, 533, 656, 832, 1066, 1312, 2132, 2624, 4264, 8528, 17056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34099 and 34112. The biggest common factor number is the GCF number.
So the greatest common factor 34099 and 34112 is 13.

Also check out the Least Common Multiple of 34099 and 34112