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Dividend = Divisor x Quotient. Therefore, the remainder is the number that is left when a dividend is not completely divisible by the divisor. Therefore, we can say: Dividend = Divisor x Quotient + Remainder. Examples are: 12 ÷ 5 = 2 Remainder 2 since 5 x 2 = 10 and 10 + 2 = 12. 33 ÷ 10 = 3 Remainder 3, since 10 x 3 = 30 and 30 + 3 = 33.
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Jul 31, 2024 · First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder.
The meaning of remainder is the leftover value or the remaining part after a division problem is called a remainder. In a division problem, there are two cases. When a number is completely divisible by another number: In this case, we are not left with anything at the end of the division.
- 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.
May 23, 2023 · When a number is divided by \(1\), the remainder is always \(0\). When a number is divided by itself, the remainder is always \(0\). If we add the remainder and the product of the divisor and quotient, we get the dividend. If two numbers have the same remainder when divided by a third number, their difference is divisible by that number.
The leftover squares are the remainder and show why the division of 14 by 4 leaves a remainder of 2. Note that this also shows why the remainder is always either 0, 1, 2, or 3 upon dividing by 4. An even number is an integer that leaves a remainder of \ (0\) upon division by \ (2\). An odd number is an integer that leaves a remainder of \ (1 ...
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The number that is divided is known as the dividend, and the number that divides the dividend is the divisor. If a number is completely divisible by the divisor, then the remainder is zero. But if it is not completely divisible by the divisor, there will be a number left behind. For example, when 7 is divided by 3, the number 7 is not ...
