Question

a number when successively divided by 7 and 8 leaves remainder 3 and 5. What is the remainder when the same number is divided by 56?​

Answer 1

Given Question :-

• A number when successively divided by 7 and 8 leaves remainder 3 and 5. What is the remainder when the same number is divided by 56?

Given :-

• A number when successively divided by 7 and 8 leaves remainder 3 and 5.

To Find :-

• The remainder when the same number is divided by 56.

Concept Used :-

$\boxed{ \red{ \sf \: Dividend = Divisor × Quotient + Remainder }}$

Solution :-

$: \implies \: \tt \: Let \: the \: \: number \: be \: x.$

Understanding the statement :-

Here, we divide a number 'x' by the first divisor, then the quotient by the second divisor, then the 2nd quotient by 3rd divisor and so on.

In this case as number was successively divided by 7 and 8 leaving remainders 3 & 5 respectively.

Let's do it now !!

Step :- 1

If number 'x' leaves remainder 3 when divided by 7,

$\sf \: then \: it \: can \: be \: expressed \: as  \: \red{ \bf \: (7m+3). }$

$\sf \: Now \: \red{ \bf \: 'm' } \: is \: the \: quotient \: after \: first \: division.$

Step :- 2

When ‘m' is divided by 8, it leaves remainder 5.

$\sf \: So, \: \red{ \bf \: ‘m' } \: can \: be \: expressed \: as  \: \red{ \bf \: (8k+5)}$

$\tt \: Thus \: \: x \: = \:  [7 \times (8k+5) + 3]$

$: \implies \: \tt \: x \: = \: 56k \: + \: 35 \: + \: 3$

$: \implies \: \tt \: x \: = \: 56k \: + 38$

☆ Now when the number 'x' is divided by 56,

$: \implies \: \tt \: the \: remainder \: will \: be \: \red{ \rm \: 38}$