What is the remainder of 45 divided by 4?
The Correct Answer and Explanation is:
To find the remainder of 45 divided by 4, we start with the division process itself. The mathematical operation can be represented as:
[
45 \div 4
]
When we perform the division, we want to find out how many times 4 can fit into 45 without exceeding it. If we calculate:
[
4 \times 11 = 44
]
This indicates that 4 can fit into 45 a total of 11 times, which gives us a product of 44. Now, we need to find the difference between the original number (45) and this product (44):
[
45 – 44 = 1
]
Therefore, when 45 is divided by 4, it leaves a remainder of 1. In mathematical terms, we can express this using the modulo operation:
[
45 \mod 4 = 1
]
This means that 1 is the remainder when 45 is divided by 4.
Explanation of Remainders
Remainders arise in division when the dividend (the number being divided) is not perfectly divisible by the divisor (the number dividing). In this case, the divisor is 4. A remainder is the amount left over after division, which cannot be further divided by the divisor without resulting in fractions or decimals.
In practical applications, finding remainders is crucial in various areas such as computer science, cryptography, and modular arithmetic, where operations wrap around after reaching a certain value (the modulus). For example, in computing, remainders can determine whether numbers are even or odd, or help in cycle detection.
To further illustrate, if we consider a group of 45 objects and want to distribute them into groups of 4, we can form 11 complete groups, each containing 4 objects. After distributing 44 objects, we are left with one object that cannot form a complete group, resulting in a remainder of 1.
Thus, the remainder when dividing 45 by 4 is:
[
\text{Remainder} = 1
]