# 4.3.2. Divisibility

Find the greatest number that is divisible by 5 and 3 and formed from 4 different digits.

• A
9 870
• B
1 230
• C
9 990
• D
9 876

### Example

Find the greatest number that is divisible by 5 and 3 and formed from 4 different digits.

### Solution

Use divisibility rules:

• A whole number is divisible by 5 if its units digit is 0 or 5.
• A whole number is divisible by 3 if the sum of its digits is divisible by 3.

Try two possible answers: one with 5 as the units digit, and one with 0 as the units digit. Then compare to find the greatest possible number.

If the digit 5 is in the units place, the greatest possible thousands digit is 9 and the greatest possible hundreds digit is 8. The only remaining digit that will result in a sum of digits that is divisible by 3 is 2. (, and 24 is divisible by 3.) So, the greatest possible number with 5 as the units digit is .

If the digit 0 is in the units place, the greatest possible thousands digit is 9 and the greatest possible hundreds digit is 8. The greatest remaining digit that will result in a sum of digits that is divisible by 3 is 7. (, and 24 is divisible by 3.) So, the greatest possible number with 0 as the units digit is .

, so the answer is .

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