What is a Divisor?
A divisor is a number that divides the dividend into equal groups. We often come across three terms in an operation involving division: dividend, divisor, and quotient.
We can write the terms as follows:
Dividend ÷ Divisor = Quotient
From the following image, you can see the different ways a divisor has been represented in a division problem.
During the division operation, we also come across the term ‘remainder’ that is the result of the divisor dividing a number incompletely. Hence the remainder is part of the result along with the quotient.
How to find a Divisor?
We can find a divisor of any division problem by either of the following formulas:
- Divisor = Dividend ÷ Quotient
- If there is a remainder which is not a zero, divisor = (Dividend – Remainder) ÷ Quotient
What is the difference between Divisor and Factor?
As we have learned, a divisor is a number that divides the dividend. Now if the divisor is able to divide the dividend completely without any remainder, the divisor is expressed as the factor of that particular number. As a result, every factor of any number is a divisor, but not all divisors are necessarily factors of the numbers.
Important Points on the Divisor
- A divisor cannot be zero because when any number is divided by zero the result is undefined.
- A division formula stays true even if we swap the quotient and the divisor.
- When we divide zero by any divisor the result is always zero.
- When the quotient and dividend is same this means the divisor is 1. For example, 30 ÷ 1 = 30
- When the dividend and the divisor are same in a division problem, the quotient is 1. For example, 30 ÷ 30 = 1
- A quotient is a number that is obtained upon dividing a dividend by a divisor, and any number that is left over after the division is called the remainder.
- The remainder is always smaller than the divisor.
- When the remainder is zero, it means the divisor has completely divided the dividend.
- When the divisor is greater than the dividend, then the resultant number will be a decimal number. For example, 35 ÷ 100 = 0.35
Solved Divisor Examples
Example 1: Find the divisor when the dividend is 459 and the quotient is 3.
Answer: We know that the dividend is 459 and the quotient is 3. According to the formula, divisor = dividend ÷ quotient
Now, let us substitute the values in the formula.
Divisor = 459 ÷ 3
= 153
Thus, the divisor is 153.
Example 2: David is planning to donate 560 food packets among 28 families. How many food packets need to be grouped together before the distribution?
Answer: According to the sum, the dividend is 560 and the quotient is 28. So, we have to find the divisor which is the count of food packets to be distributed among the families.
The formula to find the divisor is, divisor = dividend ÷ quotient
Now, by substituting the values in the formula, we get,
Divisor = 560 ÷ 28
= 20
Hence, 20 food packets will be donated to each family by David.
Example 3: Find the divisor when the dividend is 630, the remainder is 9 and the quotient is 9.
Answer: As you can see, the dividend given here is 630, the remainder is 9 and the quotient is 9. We can apply the formula for getting the divisor which we have learned previously.
Divisor = (Dividend – Remainder) ÷ Quotient
= (630 – 9) ÷ 9
= 621 ÷ 9
= 69
Therefore, the divisor is 69.
Yes, a number can be a divisor of itself. The quotient will be 1 and remainder will be 0 in such cases. Let us take an example of 4. 4 is divided by 4 to obtain the quotient as 1 and the remainder will be zero.
A fraction is expressed as a/b and the denominator, ‘b’ is regarded as the divisor. For example, 3/4 is a fraction where ‘4’ is the divisor.