Definition Formula and Solved Examples of Divisor Dividend Quotient and Remainder
The dividend-quotient formula shows the relationship between the dividend, the divisor, the quotient and the remainder, which is one of the main aspects of division. Division is the process of dividing a number into equal parts, leaving a remainder if the number cannot be further divided. The quotient formula of the remainder of division is an important rule in division. Let us learn more about these concepts ahead!
Parts of a Division
What Is the Divisor Dividend Quotient Remainder?
Divisor
A divisor is a number that divides the other number in the calculation. The divisor definition states that it is the term performing the division operation on the dividend. For example, when we divide the number 28 by the number 7, 7 is called the divisor, whereas the number 28 is called the dividend.
The formula for Divisor = (Dividend - remainder) ÷ Quotient
Dividend
A dividend is a whole number or the number of things that need to be divided into certain equal parts. Dividend is the number that is to be divided by the divisor.
The formula for Dividend = Divisor x Quotient + Remainder
Quotient
When you divide two numbers, the result of their division, called a quotient, will be a whole number. If the two numbers have no remainder when divided, they are called "perfect" factors and their quotient is their "product".
The formula for Quotient = Dividend ÷ Divisor.
Remainder
In Mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
The formula for Remainder = dividend - (divisor × quotient)
For example, 75 divided by 9 gives 8 as a quotient and 3 as a remainder.
Divisor Dividend Quotient and Remainder
Where Are Dividend, Divisor, Quotient and Remainder Used in Maths?
The divisor is used in the decimal system to convert a decimal number into fractions. The quotient is used in the multiplication of two whole numbers: for example, 4×5=20, which was simplified from $4 \times 5=20\Rightarrow \dfrac{(4 \times 10)}{2}$.
Solved Examples
Q 1 Divide 217 by 4.
Ans: $\dfrac{217}{4}$
Here, Dividend = 217
Divisor = 4
Quotient = 54
Remainder = 1
Q 2 Find the remainder when the dividend is 75, the divisor is 5 and the quotient is 15.
Ans: Given, dividend = 75, divisor = 5, quotient = 15 and let the remainder be x
75 = 5 × 15 + x
75 = 75 + x
x = 75 - 75
x = 0
Therefore, by using the formula we obtained the remainder which is 0. Remainder = 0
Q 3 Find the remainder when the dividend is 63, the divisor is 2 and the quotient is 31.
Ans: Given, dividend = 63, divisor = 2, quotient = 31 and let the remainder be x
63 = 2 × 31 + x
63 = 62 + x
x = 63 - 62
x = 1
Q 4 Divide 5679 by 7.
Ans: $\dfrac{5679}{7}$
Here, Dividend = 5679
Divisor = 7
Quotient = 811
Remainder = 2
Q 5 Find the remainder when the dividend is 57, the divisor is 8 and the quotient is 7.
Ans: Given, dividend = 75, divisor = 5, quotient = 15 and let the remainder be x
57 = 8 × 7 + x
57 = 56 + x
x = 57 -56
x = 1
Therefore, by using the formula we obtained the remainder which is 1. Remainder =1
Practice Questions
Q 1 Divide 120 by 5 and find the quotient and the remainder.
Ans: Quotient = 24
Remainder = 0
Q 2 Find the dividend when the remainder is 1, the divisor is 3, and the quotient is 31.
Ans: Dividend = 94
Q 3 Find the remainder when the dividend is 55, the divisor is 3 and the quotient is 18.
Ans: Remainder = 1
Summary
In conclusion, the number which is getting divided here is called the dividend. The number which divides a given number is the divisor. Also, the number which we get as a result is known as the quotient. The divisor which does not divide a number completely produces a number, which is referred to as remainder. We now hope you have a clear understanding of divisor, dividend, quotient and remainder.
FAQs on Divisor Dividend Quotient and Remainder in Division
1. What are divisor, dividend, quotient, and remainder?
The dividend is the number being divided, the divisor is the number that divides, the quotient is the result, and the remainder is what is left over. In a division statement:
- Dividend ÷ Divisor = Quotient + Remainder
- Example: 17 ÷ 5 = 3 remainder 2
- Here, 17 is the dividend, 5 is the divisor, 3 is the quotient, and 2 is the remainder.
2. What is the formula relating dividend, divisor, quotient, and remainder?
The formula is Dividend = (Divisor × Quotient) + Remainder. This is called the division algorithm.
- The remainder must satisfy: 0 ≤ Remainder < Divisor
- Example: 29 ÷ 4 = 7 remainder 1
- Check: 4 × 7 + 1 = 28 + 1 = 29
3. How do you find the quotient and remainder in division?
To find the quotient and remainder, divide the dividend by the divisor and identify the whole number result and leftover value.
- Step 1: Divide the numbers.
- Step 2: The whole number part is the quotient.
- Step 3: Subtract (Divisor × Quotient) from Dividend to get the remainder.
- Example: 23 ÷ 6 = 3 remainder 5
4. What is the difference between divisor and dividend?
The dividend is the number being divided, while the divisor is the number you divide by. In the division 40 ÷ 8 = 5:
- 40 is the dividend.
- 8 is the divisor.
- 5 is the quotient.
5. What is a remainder in maths?
A remainder is the amount left over after division when the dividend is not exactly divisible by the divisor. It always satisfies:
- 0 ≤ Remainder < Divisor
- Example: 15 ÷ 4 = 3 remainder 3
6. Can the remainder be greater than the divisor?
No, the remainder is always less than the divisor. If the remainder is equal to or greater than the divisor, the division is incomplete or calculated incorrectly.
- Correct condition: 0 ≤ Remainder < Divisor
- Example: In 22 ÷ 5, remainder is 2 (not 7 or 5).
7. How do you check if a division problem is correct?
You can check a division using the formula Dividend = (Divisor × Quotient) + Remainder. Follow these steps:
- Step 1: Multiply divisor and quotient.
- Step 2: Add the remainder.
- Step 3: Compare the result with the dividend.
- Example: 34 ÷ 6 = 5 remainder 4 → 6 × 5 + 4 = 34 ✅
8. What happens when the remainder is zero?
When the remainder is zero, the dividend is exactly divisible by the divisor. This means:
- The division gives a whole number quotient.
- The divisor is a factor of the dividend.
- Example: 24 ÷ 6 = 4 remainder 0
9. Can you give a real-life example of divisor, dividend, quotient, and remainder?
A real-life example is sharing objects equally among people. Suppose 19 chocolates are shared among 4 children:
- Dividend = 19 chocolates
- Divisor = 4 children
- Quotient = 4 chocolates each
- Remainder = 3 chocolates left
10. What is the division algorithm in maths?
The division algorithm states that for any integers a and b (b ≠ 0), there exist unique integers q and r such that a = bq + r and 0 ≤ r < b. Here:
- a = dividend
- b = divisor
- q = quotient
- r = remainder
