Table of contents  
Introduction  
Basic Remainder Theorem  
All possible types of Question on Reminder  
Some Special Cases  
Remainder Theorem and divisibility MCQs 
Let us understand this with the help of an example:
Ex 1: Find the remainder when (361*363) is divided by 12.
Steps:
Ex 2: Find the remainder when 10^{6} is divided by 7, i.e. (10^{6}/7)R.
Solution:
Q.1. What is the remainder when the product 1998 × 1999 × 2000 is divided by 7?
Ans:
Q.2. What is the remainder when 2^{2004} is divided by 7?
Ans:
Q.3. What is the remainder when 2^{2006} is divided by 7?
Ans:
Q.4. What is the remainder when 25^{25} is divided by 9?
Ans:
Q5. What is the remainder when 3^{444} + 4^{333} is divided by 5?
Ans: The dividend is in the form a^{x} + b^{y} . We need to change it into the form a^{n} + b^{n}.
Q6. If 2x ^{3 }3x ^{2 }+ 4x + c is divisible by x – 1, find the value of c.
Ans: Since the expression is divisible by x – 1, the remainder f(1) should be equal to zero.
Or 2 – 3 + 4 + c = 0, or c = 3.
Q7. What is the remainder when n^{7} – n is divided by 42?
Ans: Since 7 is prime, n^{7} – n is divisible by 7.
Q8. Find the remainder when 16! Is divided by 17.
Ans: 16! = (16! + 1) 1 = (16! + 1) + 16 – 17
Q9. How many numbers between 1 and 400, both included, are not divisible either by 3 or 5?
Ans: We first find the numbers that are divisible by 3 or 5. Dividing 400 by 3 and 5, we get the quotients as 133 and 80 respectively.
179 videos158 docs113 tests

1. What is the Basic Remainder Theorem? 
2. What are the possible types of questions on the Remainder Theorem? 
3. What are some special cases of the Remainder Theorem? 
4. How can the Remainder Theorem be used to test for divisibility? 
5. Can you provide multiplechoice questions (MCQs) related to the Remainder Theorem and divisibility? 
179 videos158 docs113 tests


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