What least number should be added to 1056, so that the sum is completely divisible by 23?

What least number should be added to 1056, so that the sum is completely divisible by 23?

To find the least number that should be added to 1056 so that the sum is completely divisible by 23, we can use the concept of remainder.

Step 1: Calculate the remainder when 1056 is divided by 23: 1056 divided by 23 gives a quotient of 45 and a remainder of 21.

Step 2: Determine the number to be added to 1056: To make the sum completely divisible by 23, we need to find the difference between the divisor (23) and the remainder (21).

23 - 21 = 2

Therefore, the least number that should be added to 1056 is 2 so that the sum is completely divisible by 23.

 

Step By Step Explanation:

To understand this concept, we'll explore the concepts of division, quotient, remainder, and divisibility.

Step 1: Understanding Division and Remainder When we divide two numbers, the quotient represents the number of times the divisor can be divided into the dividend evenly, and the remainder represents the amount left over.

In this case, we have 1056 as the dividend and 23 as the divisor. When we divide 1056 by 23, we can express it as follows:

1056 ÷ 23 = Quotient + Remainder

Step 2: Calculate the Remainder when 1056 is divided by 23 To find the remainder, we perform the division operation:

1056 ÷ 23 = 45 with a remainder of 21

This means that 23 can be divided into 1056 exactly 45 times, leaving a remainder of 21.

Step 3: Determining the Number to be Added To make the sum completely divisible by 23, we need to find the smallest number that, when added to 1056, results in a sum that is divisible by 23.

In this case, since the remainder is 21 and we want to achieve a completely divisible sum, we need to determine the difference between the divisor (23) and the remainder (21):

23 - 21 = 2

Hence, the least number that should be added to 1056 to obtain a sum that is completely divisible by 23 is 2.

Explanation: When we divide 1056 by 23, we obtain a quotient of 45 and a remainder of 21. This means that 23 can be divided into 1056 exactly 45 times, leaving a remainder of 21. When we add 2 to 1056, the sum becomes 1058. Now, if we divide 1058 by 23, we get a quotient of 46 with no remainder. Thus, the sum of 1058 is completely divisible by 23.

In this scenario, adding any number smaller than 2 to 1056 would not result in a completely divisible sum when divided by 23. Therefore, the least number to be added is 2 to achieve the desired divisibility.

Conclusion: To find the least number that should be added to 1056 so that the sum is completely divisible by 23, we calculated the remainder when dividing 1056 by 23. The remainder was 21. By finding the difference between the divisor (23) and the remainder (21), we determined that adding 2 to 1056 would result in a sum that is completely divisible by 23. This concept of division, quotient, remainder, and divisibility helps us identify the smallest number needed to achieve the desired divisibility condition.

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