What is the Remainder of 25 divided by 4?
The Correct Answer and Explanation is :
To find the remainder of 25 divided by 4, we can use the process of division. When we divide one number by another, the quotient is the whole number result, and the remainder is what’s left over after multiplying the quotient by the divisor and subtracting that from the original number.
Here’s how to break it down:
- Division: Start by dividing 25 by 4.
- 4 goes into 25 a total of 6 times, since ( 4 \times 6 = 24 ).
- The next whole number, 7, would give ( 4 \times 7 = 28 ), which is greater than 25, so we know that 6 is the largest whole number we can use for the division.
- Finding the Remainder: Now, we need to find out how much is left after we take 24 away from 25:
- Subtract the product of the divisor (4) and the quotient (6) from the original number (25):
[
25 – 24 = 1
] - Thus, the remainder is 1.
- Understanding Remainders: The remainder tells us what is left over after you’ve divided a number into equal parts. In this case, after dividing 25 into groups of 4, we have 1 left over, which cannot form another complete group of 4.
- Remainders in Division: Remainders are a fundamental concept in arithmetic and number theory. They come into play in various mathematical applications, such as modular arithmetic, where we often express results as remainders. The notation ( a \mod b ) represents the remainder when ( a ) is divided by ( b ).
In conclusion, when dividing 25 by 4, the quotient is 6, and the remainder is 1. This process demonstrates how division works and provides insight into the relationship between numbers. The final answer is:
The remainder of 25 divided by 4 is 1.