What is the Maximum number Divisible by 9 that can be formed using the Digits 6, 4, 8, 1 without repetition?

What is the Maximum number Divisible by 9 that can be formed using the Digits 6, 4, 8, 1 without repetition?

To determine the maximum number of distinct numbers that can be formed using the digits 6, 4, 8, and 1, without repetition, and that are divisible by 9, follow these steps

Begin by adding all the digits together

6 + 4 + 8 + 1 = 19

According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is divisible by 9.

Here, the sum of the digits is 19. Since 19 is not divisible by 9, any number formed using these digits will not be divisible by 9.

Since the sum of the digits is not divisible by 9, it is impossible to form any number using all four digits that will be divisible by 9. Hence, no such numbers can be formed.

How to Find Numbers Divisible by using Specific Digits?

In mathematics, determining whether numbers formed from a given set of digits are divisible by a specific number, like 9, involves a few key steps. This process often uses the properties of divisibility and basic arithmetic.

Sum of Digits:

The first step is to calculate the sum of the digits. This is important because for a number to be divisible by 9, the sum of its digits must also be divisible by 9. This is a fundamental rule in divisibility.

Check Divisibility:

After finding the sum of the digits, you need to check if this sum is divisible by 9. If the sum is divisible by 9, then any permutation of these digits will form a number that is divisible by 9.

Permutations and Repetition:

When using all the given digits to form numbers, each digit must be used exactly once, without repetition. The permutations of these digits will create different numbers. However, if the sum of the digits is not divisible by 9, none of these numbers will be divisible by 9. This approach is useful for solving problems related to digit-based divisibility and permutations. It helps in understanding how numbers behave under certain conditions and in solving puzzles or mathematical problems involving digit constraints.