Question

What is the largest three-digit number divisible by 24 and 54?

Answer 1

The largest three-digit number divisible by 24 and 54 is:

• 864

Explanation:

To identify the largest number what I did was dividing 999 (the largest whole three-digit number of all) in the first number given (24):

• 
  `(999)/(24)=41.625`

With this number, you know that you must multiply 24 by a number like 41 or less until you find a number that can be divisible by 54 and obtain a whole number, so:

• 24*41= 984/54= 18.22 (how the number obtained is not a whole number, this is not the correct).

• 24*40= 960/54= 17.77 (this is not).
• 24*39= 936/54= 17.33 (this is not).
• 24*38= 912/54= 16.88 (this is not).
• 24*37=888/54= 16.44 (this is not).
• 24*36= 864/54= 16 (This is the correct).

Now, you have identified that the number 864, you can prove it by dividing this in 24 and 54:

• 
  `(864)/(24)=36`
• 
  `(864)/(54)= 16`