Question

a number when divided by 483 gives a remainder 79 .what remainder would be obtained by dividing the same number by 23 ?​

Answer 1

Answer:

Dividend is the number itself

Divisior is 342

Remainder is 47

Quotient obviously would be any integer (let it be k)

Now, further

342k + 47 = 19*18k + (38+9)

= 19*18k + 19*2 + 9

= 19*(18k+2) + 9

= 19m + 9 (here m is any other integer)

Now again recall that

Dividend=Divisior*Quotient+Remainder

Here;

Dividend is the number itself

Divisior is 19

Quotient is m (obviously an integer)

Remainder is 9....!!

Hope this helps you with your problem...!!

Cheers...!!

47 divided by 19 would leave a remainder of 9 ( 19*2+9)

Such type of question are asked quite often, you just divide the remainder given already in the question by the divisor (latter) after checking if the divisor already given is divisible by the latter divisor.

Phew! quite a long sentence it was.

Anways 342 is 19*18. If you mug up till 20 it really helps. For eg 13*14 is 182

Thanks for the A2A.

PS:

Answer: Just divide 21 by 18, remainder is 3.

Answer: Just divide 25 by 11, remainder =3 ( 5-2 is better than checking 25-22 )

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Let the number be n.

We have n mod

So, you can write n as x for some integer x

Also,

So, n x

+ 47 for some integer k.

where u = k + 2

So, mod

Therefore, the remainder is .

Hope that helps. :)

If a number is divisible by 342, the remainder is 47. What is the remainder of the number given by dividing this number from 18?

A number, when divided by 114 leaves a remainder of 21. If the same number is divided by 19, then what will the remainder be?

A number when divided by 162 leaves a remainder 21 it's same number divided by 18 then what could be the remainder?

The first thing to note is that 342 = 19*18. So let the number be x.

So, x = 342*n + 47

x = 342*n + 38 + 9

x = 19*(18n + 2) + 9

Clearly, when divided by 19, the remainder is 9.

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Shortest method

dividend = divisor*quotient + remainder

for quotient (say 1)

required no. = 342*1 + 47

=389

remainder = 389 mod 19

= 9 ansr.

u can try it for 1,2,3,4,..n as well. same answer

Let the given number be x and a is remainder when x is divided by 19.

Thus x=a mod(19).It is also given that x leaves remainder 47 when divided br 342.Thus x=47 mod(342).

x=a mod(19) and x=47 mod(342)=>

there exist positive integers p and q such that

x-47=342p and x-a=19q

=>a-47=19(18p-q) =19b

Where b=18p-q

a-47=19b=>a=9 and b=-2

Now 18p-q=b=-2=>p=1 and q=20

Hence x=342+47=389 and a=19*(-2)+47=9.

Thus same number leaves remainder 9 when divided by 19.

We can write 342 = 19*18

Let's say we divide x by 342 and get a remainder of 47, so we can write

x = (some whole number)*342 +47

Now,when we divide x by 19 we have

x/19 = (some whole number)*342/19 + 47/19

now the first term is completely divided by 19,so we will get remainder only from second term which is 47/19 .

Now 47 = 19*2 + 9

so finally we have remainder = 9