What is the smallest number that can be subtracted from 40658to make it divisible by 11
To make a number divisible by 11, the difference between the sum of its digits at odd positions and the sum of its digits at even positions must be divisible by 11.
For the number 40658, the sum of the digits at odd positions is 4 + 6 + 8 = 18, and the sum of the digits at even positions is 0 + 5 = 5.
Therefore, the difference between these sums is 18 - 5 = 13, which is not divisible by 11.
To make it divisible by 11, we need to subtract a number from 40658 to reduce this difference.
The smallest number that can be subtracted from 40658 to make it divisible by 11 is 2.
40658 - 2 = 40656
The sum of the digits at odd positions is 4 + 6 + 6 = 16, and the sum of the digits at even positions is 0 + 5 = 5.
The difference between these sums is 16 - 5 = 11, which is divisible by 11.
Therefore, 40656 is divisible by 11.
To find the smallest number that can be subtracted from 40658 to make it divisible by 11, we first need to determine how the number 40658 is related to divisibility by 11.
A number is divisible by 11 if the difference between the sum of its odd-placed digits and the sum of its even-placed digits is divisible by 11.
In the case of 40658, the odd-placed digits are 4, 6, and 8, which add up to 18. The even-placed digits are 0 and 5, which add up to 5.
The difference between the sum of the odd-placed digits and the sum of the even-placed digits is 18 - 5 = 13.
Since 13 is not divisible by 11, we need to find the smallest number that, when subtracted from 40658, makes the difference divisible by 11.
To do this, we can find the remainder of dividing 13 by 11.
13 divided by 11 is 1 with a remainder of 2.
Therefore, to make the difference divisible by 11, we need to subtract 2 from 40658.
The smallest number that can be subtracted from 40658 to make it divisible by 11 is 2.
To find the smallest number that can be subtracted from a given number to make it divisible by another number, you need to determine the remainder when the given number is divided by the desired divisor (in this case, 11).
1. Determine the remainder: Divide 40658 by 11. The remainder is the amount that needs to be subtracted to make the number divisible by 11.
40658 ÷ 11 = 3696 remainder 2
2. Calculate the amount to subtract: To make 40658 divisible by 11, you need to subtract the remainder (2) from it.
40658 - 2 = 40656
Therefore, the smallest number that can be subtracted from 40658 to make it divisible by 11 is 2.