What is the Greatest Common Factor of 32400 and 32419?

Greatest common factor (GCF) of 32400 and 32419 is 1.

GCF(32400,32419) = 1

We will now calculate the prime factors of 32400 and 32419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32400 and 32419.

How to find the GCF of 32400 and 32419?

We will first find the prime factorization of 32400 and 32419. After we will calculate the factors of 32400 and 32419 and find the biggest common factor number .

Step-1: Prime Factorization of 32400

Prime factors of 32400 are 2, 3, 5. Prime factorization of 32400 in exponential form is:

32400 = 2⁴ × 3⁴ × 5²

Step-2: Prime Factorization of 32419

Prime factors of 32419 are 17, 1907. Prime factorization of 32419 in exponential form is:

32419 = 17¹ × 1907¹

Step-3: Factors of 32400

List of positive integer factors of 32400 that divides 32400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200

Step-4: Factors of 32419

List of positive integer factors of 32419 that divides 32400 without a remainder.

1, 17, 1907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32400 and 32419. The biggest common factor number is the GCF number.
So the greatest common factor 32400 and 32419 is 1.

Also check out the Least Common Multiple of 32400 and 32419