The largest remainder you can have when you divide by 25 is 24.
Understanding Remainders
When you perform division, you divide a number (the dividend) by another number (the divisor) to get a result (the quotient) and sometimes a leftover amount, which is called the remainder.
The fundamental rule of division with whole numbers states that the remainder must always be a whole number less than the divisor.
- Dividend = ( Divisor × Quotient ) + Remainder
- The Remainder must be greater than or equal to 0.
- The Remainder must be less than the Divisor.
In this question, the divisor is 25. Therefore, the remainder must be less than 25.
The Largest Possible Remainder
According to Chegg.com, "The Greatest Possible Whole Number Remainder when you divide a number by 25 is 24 and can never be g...". This confirms the mathematical rule.
Since the remainder must be a whole number less than 25, the possible whole number remainders are 0, 1, 2, ..., all the way up to 24.
The largest number in this list is 24.
Examples
Here are a few examples illustrating different remainders when dividing by 25:
| Division | Calculation | Quotient | Remainder |
|---|---|---|---|
| 50 ÷ 25 | (25 × 2) + 0 | 2 | 0 |
| 51 ÷ 25 | (25 × 2) + 1 | 2 | 1 |
| 74 ÷ 25 | (25 × 2) + 24 | 2 | 24 |
| 75 ÷ 25 | (25 × 3) + 0 | 3 | 0 |
| 99 ÷ 25 | (25 × 3) + 24 | 3 | 24 |
| 100 ÷ 25 | (25 × 4) + 0 | 4 | 0 |
Notice how the remainder cycles from 0 up to 24 and then goes back to 0 when the dividend is a multiple of 25.
Why Can't the Remainder be 25 or More?
If you had a remainder of 25 or more when dividing by 25, it would mean you could have included another group of 25 in your quotient.
For instance, if you divided 75 by 25 and thought the remainder was 25 (with a quotient of 2), the calculation would look like:
75 = (25 × 2) + 25
However, since 25 is equal to the divisor, you can take one more group of 25 out of the remainder and add it to the quotient:
75 = (25 × 3) + 0
This demonstrates that any remainder of 25 or greater indicates the division process is not complete and the remainder is not the smallest possible non-negative value.
In summary, the largest possible whole number remainder when dividing by any whole number 'n' is always 'n-1'. For a divisor of 25, the largest remainder is 25 - 1 = 24.
