What is the Greatest Common Factor of 43500 and 43520?

Greatest common factor (GCF) of 43500 and 43520 is 20.

GCF(43500,43520) = 20

We will now calculate the prime factors of 43500 and 43520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43500 and 43520.

How to find the GCF of 43500 and 43520?

We will first find the prime factorization of 43500 and 43520. After we will calculate the factors of 43500 and 43520 and find the biggest common factor number .

Step-1: Prime Factorization of 43500

Prime factors of 43500 are 2, 3, 5, 29. Prime factorization of 43500 in exponential form is:

43500 = 2² × 3¹ × 5³ × 29¹

Step-2: Prime Factorization of 43520

Prime factors of 43520 are 2, 5, 17. Prime factorization of 43520 in exponential form is:

43520 = 2⁹ × 5¹ × 17¹

Step-3: Factors of 43500

List of positive integer factors of 43500 that divides 43500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 29, 30, 50, 58, 60, 75, 87, 100, 116, 125, 145, 150, 174, 250, 290, 300, 348, 375, 435, 500, 580, 725, 750, 870, 1450, 1500, 1740, 2175, 2900, 3625, 4350, 7250, 8700, 10875, 14500, 21750

Step-4: Factors of 43520

List of positive integer factors of 43520 that divides 43500 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 128, 136, 160, 170, 256, 272, 320, 340, 512, 544, 640, 680, 1088, 1280, 1360, 2176, 2560, 2720, 4352, 5440, 8704, 10880, 21760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43500 and 43520. The biggest common factor number is the GCF number.
So the greatest common factor 43500 and 43520 is 20.

Also check out the Least Common Multiple of 43500 and 43520