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Karthik

· started a discussion

· 1 Months ago

Cant interpret what you are saying.. (Question: 217520.0 )

I want to learn this remainder and divisible type of problem from root, can you tell where can i get a clear idea of all this about??!!

Question:
1921 + 2121 is divisible by –
Options:
A) 10 only 
B) 20 only 
C) Both 10 and 20
D) Neither 10 nor 20
Solution:
Ans: (c)

1921 + 2121 = (20 – 1)21 + (20 + 1)21

Remainder = –1 + 1

= 0

So, (1921 + 2121) is divisible by 20 and 10.

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

Concept of Remainder:
Supposing a number N is divided by another number “x”; if the quotient obtained is “Q” and the remainder obtained is “R”, then the number can be expressed as N=Qx+R



For example, suppose 8 is divided by 3

In this case, N=8, x=3. 3×2=6, which is 2 less than 8. hence Q=2 and R=(8-6)=2 Hence 8=2×3+2




Basic Remainder Theorem:

Basic remainder theorem is based on product of individual remainders.

If R is the remainder of an expression( p*q*r)/X, and pR, qR and rR are the remainders when p,q and r are respectively divided by X,

then it can be said that ((pR x qR x rR ))/X, will give the same remainder as given by (p*q*r)/X

Let us understand this with the help of an example



#Q01. Find the remainder when (361*363) is divided by 12.

Steps:

1) Take the product of individual remainders, i.e. 361/12|R =1 and 363/12|R= 3

2) Find the remainder when you divide that product by the number (361*363)/12|R= (1*3)/12|R. answer= 3

This is Basic Remainder theorem put across in Numbers




#Q02. Find the remainder when 106 is divided by7 i.e. (106/7)R.

Solution:

106=103x103

Thus(106/7)R = (103/7 x 103/7)R = ((6 * 6)/7)R = (36/7)R = 1.

So the remainder is 1


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