Question

If 1, 2, and 4 are three of the digits of the four digit number n, and if n is divisible by 4, find the greatest possible value of n. (40pts) Explain how you know you have the largest possible number n. (60 pts)

Answer 1

Answer: n = 412

Explanation:

If the last two digits of a number are divisible by 4, the whole number is divisible by 4 since any multiple of 100 is divisible by 4. The largest number that can be created is 421 since the largest number is in the hundreds place and then the second largest number is in the tens place, but 21 is not divisible by 4. The second largest number, 412, still has the greatest number as the hundreds place, but the tens place is now smaller. 12 is divisible by 4, so 412 is divisible by 4. We know that 412 is the largest possible number for n because there is only one larger number than 412, which is 421 and it is not divisible by 4.

Answer 2

• The largest possible n is 9412

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Divisibility rule for 4:

• If the last two digits of a number are divisible by 4, the number is divisible by 4

We have 3 digits and the greatest number can be made by these digits is 421. But it has to be divisible by 4, hence we rearrange it to 412. Since 12 is divisible by 4, the number is divisible by 4.

Now, we choose 9 as the fourth digit. It will be a first digit from left and form the largest possible number n:

• n = 9412