What is the Greatest Common Factor of 29189 and 29200?

Greatest common factor (GCF) of 29189 and 29200 is 1.

GCF(29189,29200) = 1

We will now calculate the prime factors of 29189 and 29200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29189 and 29200.

How to find the GCF of 29189 and 29200?

We will first find the prime factorization of 29189 and 29200. After we will calculate the factors of 29189 and 29200 and find the biggest common factor number .

Step-1: Prime Factorization of 29189

Prime factors of 29189 are 17, 101. Prime factorization of 29189 in exponential form is:

29189 = 17² × 101¹

Step-2: Prime Factorization of 29200

Prime factors of 29200 are 2, 5, 73. Prime factorization of 29200 in exponential form is:

29200 = 2⁴ × 5² × 73¹

Step-3: Factors of 29189

List of positive integer factors of 29189 that divides 29189 without a remainder.

1, 17, 101, 289, 1717

Step-4: Factors of 29200

List of positive integer factors of 29200 that divides 29189 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 73, 80, 100, 146, 200, 292, 365, 400, 584, 730, 1168, 1460, 1825, 2920, 3650, 5840, 7300, 14600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29189 and 29200. The biggest common factor number is the GCF number.
So the greatest common factor 29189 and 29200 is 1.

Also check out the Least Common Multiple of 29189 and 29200