How do you find the number of different factors of number 75600?

Answer 1

Using the division method to find prime factors

1. let x be the number to be factorised
2. let p be the lowest Prime number below the square root of x (always 2, unless x is below 4)
3. Calculate x/p
4. if x/p was an integer, update the list of factors to include p and let x = x/p
5. if x > 1 and p < √x, return to step 3
6. you now have your completed list

So, to find the prime factors of 75600, just follow the instructions.

75600/2 = 37800[2] 37800/2 = 18900[2] 18900/2 = 9450[2] 9450/2 = 4725[2] 4725/2 = 2362.5 4725/3 = 1575[3] 1575/3 = 525[3] 525/3 = 175[3] 175/3 = 58.3 175/5 = 35[5] 35/5 = 7[5] 7[7]

So, 75600 = 2x2x2x2x3x3x3x5x5x7 = 24x33x52x7

A full list of factors could be arranged from this, by multiplying different prime factors together.
Ie.
75600, 37800, 25200, 18900, 15120, 12600, 10800, 9450, 8400, 7560, 6300, 5400, 5040, 4725, 4200, 3780, 3600, 3150, 3024, 2800, 2700, 2520, 2160, 2100, 1890, 1800, 1680, 1575, 1512, 1400, 1350, 1260, 1200, 1080, 1050, 1008, 945, 900, 840, 756, 720, 700, 675, 630, 600, 560, 540, 525, 504, 450, 432, 420, 400, 378, 360, 350, 336, 315, 300, 280, 270, 252, 240, 225, 216, 210, 200, 189, 180, 175, 168, 150, 144, 140, 135, 126, 120, 112, 108, 105, 100, 90, 84, 80, 75, 72, 70, 63, 60, 56, 54, 50, 48, 45, 42, 40, 36, 35, 30, 28, 27, 25, 24, 21, 20, 18, 16, 15, 14, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Answer 2

To find the number of different factors of a number, factorize the number into its prime factors. For 75600, the prime factorization is 2^4 * 3^3 * 5^2 * 7. Now, add 1 to the exponent of each prime factor and multiply the results: (4+1) * (3+1) * (2+1) * (1+1) = 5 * 4 * 3 * 2 = 120. Therefore, the number 75600 has 120 different factors.