What is the Greatest Common Factor of 32109 and 32128?

Greatest common factor (GCF) of 32109 and 32128 is 1.

GCF(32109,32128) = 1

We will now calculate the prime factors of 32109 and 32128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32109 and 32128.

How to find the GCF of 32109 and 32128?

We will first find the prime factorization of 32109 and 32128. After we will calculate the factors of 32109 and 32128 and find the biggest common factor number .

Step-1: Prime Factorization of 32109

Prime factors of 32109 are 3, 7, 11, 139. Prime factorization of 32109 in exponential form is:

32109 = 3¹ × 7¹ × 11¹ × 139¹

Step-2: Prime Factorization of 32128

Prime factors of 32128 are 2, 251. Prime factorization of 32128 in exponential form is:

32128 = 2⁷ × 251¹

Step-3: Factors of 32109

List of positive integer factors of 32109 that divides 32109 without a remainder.

1, 3, 7, 11, 21, 33, 77, 139, 231, 417, 973, 1529, 2919, 4587, 10703

Step-4: Factors of 32128

List of positive integer factors of 32128 that divides 32109 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 251, 502, 1004, 2008, 4016, 8032, 16064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32109 and 32128. The biggest common factor number is the GCF number.
So the greatest common factor 32109 and 32128 is 1.

Also check out the Least Common Multiple of 32109 and 32128