What is the Greatest Common Factor of 32400 and 32410?

Greatest common factor (GCF) of 32400 and 32410 is 10.

GCF(32400,32410) = 10

We will now calculate the prime factors of 32400 and 32410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32400 and 32410.

How to find the GCF of 32400 and 32410?

We will first find the prime factorization of 32400 and 32410. After we will calculate the factors of 32400 and 32410 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 32410

Prime factors of 32410 are 2, 5, 7, 463. Prime factorization of 32410 in exponential form is:

32410 = 2¹ × 5¹ × 7¹ × 463¹

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 32410

List of positive integer factors of 32410 that divides 32400 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 463, 926, 2315, 3241, 4630, 6482, 16205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32400 and 32410. The biggest common factor number is the GCF number.
So the greatest common factor 32400 and 32410 is 10.

Also check out the Least Common Multiple of 32400 and 32410