Question

what is the greatest four digit number that is divisible by 2 and 5

Answer 1

Step-by-step explanation:

If a number n is divisible by multiple numbers a,b,c , then n is also divisible by the least common multiple of a,b,c . The least common multiple of 2, 3, and 5 is 30, so our magic 4 digit number n is divisible by 30. For a number to be divisible by 30, it must be divisible by 3 and 10 (applying that same rule in the opposite way), so it must end in 0 (so the number is divisible by 10), and all of the digits add up to a multiple of 3 (so the number is also divisible by 3). What’s the greatest 4 digit number that fits this description? Probably 9990, because (9+9+9+0)mod3 = 0 and 9990 ends in 0. And 9990 mod 30 = 0, so it’s divisible by 30. The only greater 4 digit numbers are 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, and 9999. None of these are divisible by 10, so they cannot be divisible by 30. Therefore, 9990 is the greatest 4 digit number divisible by 2, 3, and 5.

Answer 2

SOLUTION

TO DETERMINE

The greatest four digit number that is divisible by 2 and 5

EVALUATION

Here the given numbers are 2 and 5

Now 2 and 5 are prime to each other

So LCM of 2 and 5 = 2 × 5 = 10

Now the greatest four digit number = 9999

If we divide 9999 by 10 we get 999 as quotient and 9 as remainder

Hence the required number

= 9999 - 9

= 9990

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