What is the Greatest Common Factor of 32129 and 32148?

Greatest common factor (GCF) of 32129 and 32148 is 19.

GCF(32129,32148) = 19

We will now calculate the prime factors of 32129 and 32148, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32129 and 32148.

How to find the GCF of 32129 and 32148?

We will first find the prime factorization of 32129 and 32148. After we will calculate the factors of 32129 and 32148 and find the biggest common factor number .

Step-1: Prime Factorization of 32129

Prime factors of 32129 are 19, 89. Prime factorization of 32129 in exponential form is:

32129 = 19² × 89¹

Step-2: Prime Factorization of 32148

Prime factors of 32148 are 2, 3, 19, 47. Prime factorization of 32148 in exponential form is:

32148 = 2² × 3² × 19¹ × 47¹

Step-3: Factors of 32129

List of positive integer factors of 32129 that divides 32129 without a remainder.

1, 19, 89, 361, 1691

Step-4: Factors of 32148

List of positive integer factors of 32148 that divides 32129 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 47, 57, 76, 94, 114, 141, 171, 188, 228, 282, 342, 423, 564, 684, 846, 893, 1692, 1786, 2679, 3572, 5358, 8037, 10716, 16074

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32129 and 32148. The biggest common factor number is the GCF number.
So the greatest common factor 32129 and 32148 is 19.

Also check out the Least Common Multiple of 32129 and 32148