Question

number when divided by 340 gives a remainder 47. What would be the remainder when the same number is divided by 17 ?

Answer 1

Step-by-step explanation:

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Secondary School Math 13 points

A no when divided by 342 gives a remainder 47. when the same no. divided by 19 what would be the remainder

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Answers

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As per statement 1,

The number must be of the form 342k + 47 , where k is any integer

(Try recalling what you read in younger classes, i.e.

Dividend=Divisior*Quotient+Remainder)

Here;

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*2 when divided by 19 gives the quotient 2)

= 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...!

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Answer 2

The answer is 13

GIVEN

Number when divided by 340 gives a remainder 47.

TO FIND

What would be the remainder when the same number is divided by 17 ?

SOLUTION

The above problem can be simply solved as follows;

Given,

Remainder when a number is divided by 340 = 47

Let the quotient = K

According to remainder formula;

Dividend = Divisor x Quotient + Remainder

= 340 × K + 47

The number = 340K + 47

= 17 × 20k + 17 × 2 + 13

= 17(20k + 2) + 13

Comparing with remainder formula

Divisor = 19

Quotient = 20k + 2

Remainder = 13

Hence, The answer is 13

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