What is the Greatest Common Factor of 34109 and 34128?

Greatest common factor (GCF) of 34109 and 34128 is 1.

GCF(34109,34128) = 1

We will now calculate the prime factors of 34109 and 34128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34109 and 34128.

How to find the GCF of 34109 and 34128?

We will first find the prime factorization of 34109 and 34128. After we will calculate the factors of 34109 and 34128 and find the biggest common factor number .

Step-1: Prime Factorization of 34109

Prime factors of 34109 are 23, 1483. Prime factorization of 34109 in exponential form is:

34109 = 23¹ × 1483¹

Step-2: Prime Factorization of 34128

Prime factors of 34128 are 2, 3, 79. Prime factorization of 34128 in exponential form is:

34128 = 2⁴ × 3³ × 79¹

Step-3: Factors of 34109

List of positive integer factors of 34109 that divides 34109 without a remainder.

1, 23, 1483

Step-4: Factors of 34128

List of positive integer factors of 34128 that divides 34109 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 79, 108, 144, 158, 216, 237, 316, 432, 474, 632, 711, 948, 1264, 1422, 1896, 2133, 2844, 3792, 4266, 5688, 8532, 11376, 17064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34109 and 34128. The biggest common factor number is the GCF number.
So the greatest common factor 34109 and 34128 is 1.

Also check out the Least Common Multiple of 34109 and 34128