4,320 is divisible by
a. 3
b. 9
c. 10
explain your reasoning for your choice(s).

Hello!

So our number is 4,320, and we want to know if its divisible by some numbers:

a) by 3, so we know that every number is divisible by 3 if the addition of all te decimals that conform it are a multiple of 3 ( for example 3, 6, 9, 12...), this is:

4 + 3 + 2 + 0 = 9, 9 is a multiple of 3, then 4320 is divisible by 3.

and we know that 3 * 1000 = 3000

3*400 = 1200

3*40 = 120

then 3*(40 + 400 + 1000) = 4320

then 4320/3= 1440

b) by 9.

We already know that if the addition of all the decimals is a multiple of 3, then the number is divisible by 3. We also know that 9 = 3*3, and we know that 4320/3 = 1440

now; 4320/9 = 4320/(3*3) = 1440/3

now we need to see if 1440 is divisible by 3, then we use the same method as before, 1 + 4 + 4+ 0 = 9, then 1440 is divisible by 3

c) by 10, every number that ends in a 0 is divisible by 10, here 4320/10 = 432, so dividing by 10 "removes" the last 0 in our number (and multiplying by 10 ads a 0 to the right side of our number)