What is the Greatest Common Factor of 16089 and 16100?

Greatest common factor (GCF) of 16089 and 16100 is 1.

GCF(16089,16100) = 1

We will now calculate the prime factors of 16089 and 16100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16089 and 16100.

How to find the GCF of 16089 and 16100?

We will first find the prime factorization of 16089 and 16100. After we will calculate the factors of 16089 and 16100 and find the biggest common factor number .

Step-1: Prime Factorization of 16089

Prime factors of 16089 are 3, 31, 173. Prime factorization of 16089 in exponential form is:

16089 = 3¹ × 31¹ × 173¹

Step-2: Prime Factorization of 16100

Prime factors of 16100 are 2, 5, 7, 23. Prime factorization of 16100 in exponential form is:

16100 = 2² × 5² × 7¹ × 23¹

Step-3: Factors of 16089

List of positive integer factors of 16089 that divides 16089 without a remainder.

1, 3, 31, 93, 173, 519, 5363

Step-4: Factors of 16100

List of positive integer factors of 16100 that divides 16089 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 23, 25, 28, 35, 46, 50, 70, 92, 100, 115, 140, 161, 175, 230, 322, 350, 460, 575, 644, 700, 805, 1150, 1610, 2300, 3220, 4025, 8050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16089 and 16100. The biggest common factor number is the GCF number.
So the greatest common factor 16089 and 16100 is 1.

Also check out the Least Common Multiple of 16089 and 16100