Search results
Note that the remainder always has to be less than the divisor. If it is more than the divisor, it means the long division is incomplete. Example: Divide 75 by 4. Find the remainder. Properties of a Remainder. A remainder is always less than the divisor. If one number (divisor) divides the other number (dividend) completely, then the remainder ...
The remainder is always less than the divisor. A remainder that is either greater than or equal to the divisor indicates that the division is incorrect. If one number (divisor) divides the other number (dividend) completely, then the remainder is 0. The remainder can be either greater, lesser, or equal to the quotient. ☛Related Articles
Rather than using the largest multiple less than or equal to the dividend, children may identify the closest multiple (one that is too high) or one that is less than the dividend but is too low. Add further examples using counters to explore patterns where one more is added to draw attention to the size of the remainder compared to the divisor.
- Concept of Remainder
- Properties of Remainders
- Concept of Negative Remainder
- Finding Remainder of An Expression
- Generalizations Based on Remainder Theorem
- Remainder Properties of Prime Numbers
- Remainder Properties of Composite Numbers
If a number A is divided by B, then A is the dividend and B is the divisor. There are two possibilities: 1. Either a remainder is left 2. Or No remainder is left, i.e. Remainder = 0 (means it completely divides) Let’s see both of these cases in more detail.
Addition and Remainders
If two dividends A and B, when divided by a divisor Z, leaves remainders r1 and r2 respectively, then the remainder when A + B is divided by Z is r1+r2. E.g. Remainder [185] = 3 and Remainder [315] = 1 ∴ Remainder [18+315] = 3 + 1 = 4
Subtraction and Remainders
If two dividends A and B, when divided by a divisor Z, leaves remainders r1 and r2 respectively, then the remainder when A - B is divided by Z is r1−r2. E.g. Remainder [175] = 2 and Remainder [345] = 4 ∴ Remainder [34−175] = 4 - 2 = 2
Multiplication and Remainders
If two dividends A and B, when divided by a divisor Z, leaves remainders r1 and r2 respectively, then the remainder when A × B is divided by Z is r1×r2. E.g. Remainder [185] = 3 and Remainder [315] = 1 ∴ Remainder [31×185] = 1 × 3 = 3
Remainder can be zero or some positive number less than the divisor. It can never be negative. But sometimes we encounter negative remainders. Let’s see what they mean and how to handle them with the help of an example. If 11 is the number being divided and 3 is the divisor, then we can write 11 as: 11 = 3 × 3 + 2 (here 2 is the remainder) Or 11 = ...
There are two methods to find out the remainder of any expression. 1. Cyclicity Method / Pattern Method 2. Remainder Theorem method
Generalization 1
(p+1)npwill always give 1 as the remainder for all natural values of p and n.
Generalization 2
pn(p+1)will always give 1 as the remainder, when n is even.
Generalization 3
pn(p+1)will always give p as the remainder, when n is odd.
Property 1
For any prime p>3, p2− 1 is a multiple of 24. E.g. if p = 5, then 52 − 1 = 24If p = 11, then 112− 1 = 120 (a multiple of 24)
Property 2: Fermat’s theorem
Let ‘x’ and ‘y’ be any two prime numbers. Then xy− x is always divisible by y. E.g. 23 − 2 = 6 is divisible by 3. 25 − 2 = 30 is divisible by 5. 33− 3 = 24 is divisible by 3.
Property 3: Fermat’s little theorem
Let ‘x’ and ‘y’ be any two relatively prime numbers (where ‘y’ is a prime number) Then Remainder [xy−1y] is 1. E.g. if x = 10 and y = 7 Remainder [1067] = 1 Let us double check it. Remainder [1067] = Remainder [367] = Remainder [937] = Remainder [237] = Remainder = 1
Property 1: Wilson’s theorem
If n is a composite number more than 4, then (n - 1)! will be divisible by n. E.g. if n = 6, then (6 – 1)! = 5! = 120 is divisible by 6. If n = 8, then (8 – 1)! = 7! = 5040 is divisible by 8.
Note that the remainder will always be less than the divisor; in this case, dividing by 4 will always leave a remainder that is either 0, 1, 2, or 3. To find the remainder of a number \(n\) upon division by a divisor \(d\), we first find the largest multiple of \(d\) that goes into \(n\), and the remainder \(r\) is the amount left over:
May 23, 2023 · Furthermore, we observe that the remainder is always less than the divisor, as in this case, \(3\) is less than \(4\). Remainder Definition. The concept of remainder is a crucial aspect of division, wherein it represents the digit or number that remains after completing the division process. It occurs when division cannot be completed evenly ...
People also ask
What if the remainder is less than the divisor?
What happens if a dividend is less than a divisor?
What are the properties of the remainder?
What is the relationship between dividend divisor quotient and remainder?
What does remainder mean in a division problem?
How to find the remainder using long division?
When we cannot make equal groups or share equally all the objects, the number which is left undivided is called the remainder. Remainder is always less than the divisor. So, Dividend = Divisor × Quotient + Remainder. In the above example = 9 × 2 + 1. The dividend, divisor, quotient and remainder will help us to verify the answer of division.
