What is the Greatest Common Factor of 29889 and 29900?

Greatest common factor (GCF) of 29889 and 29900 is 1.

GCF(29889,29900) = 1

We will now calculate the prime factors of 29889 and 29900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29889 and 29900.

How to find the GCF of 29889 and 29900?

We will first find the prime factorization of 29889 and 29900. After we will calculate the factors of 29889 and 29900 and find the biggest common factor number .

Step-1: Prime Factorization of 29889

Prime factors of 29889 are 3, 41. Prime factorization of 29889 in exponential form is:

29889 = 3⁶ × 41¹

Step-2: Prime Factorization of 29900

Prime factors of 29900 are 2, 5, 13, 23. Prime factorization of 29900 in exponential form is:

29900 = 2² × 5² × 13¹ × 23¹

Step-3: Factors of 29889

List of positive integer factors of 29889 that divides 29889 without a remainder.

1, 3, 9, 27, 41, 81, 123, 243, 369, 729, 1107, 3321, 9963

Step-4: Factors of 29900

List of positive integer factors of 29900 that divides 29889 without a remainder.

1, 2, 4, 5, 10, 13, 20, 23, 25, 26, 46, 50, 52, 65, 92, 100, 115, 130, 230, 260, 299, 325, 460, 575, 598, 650, 1150, 1196, 1300, 1495, 2300, 2990, 5980, 7475, 14950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29889 and 29900. The biggest common factor number is the GCF number.
So the greatest common factor 29889 and 29900 is 1.

Also check out the Least Common Multiple of 29889 and 29900