Question

A number divided by 119 leaves as 19. If the same number is divided by 17, the reminder will be

Answer 1

Hi there!
Here's the answer:

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¶¶¶ Remainder Rule-1:

¶ Condition Of this Rule Application:
• This Rule is applied to find the Remainder of smaller division, when same No. is divided by two different divisors such that ONE DIVISOR IS A MULTIPLE OF OTHER DIVISOR & also remainder for the greatest divisor is known.


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¶¶Statement :

•If remainder for greatest divisors is r &
the smaller division is d :

Case -(a) : When r > d
>> Then required remainder for smaller divisor will be
- Remainder obtained by dividing 'r' by 'd'.

Case - (b) : When r < d
>> Then required remainder for smaller divisor will be
- Remainder 'r' itself.


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Now,
¶¶ SOLUTION:

Here, Same No. is divided by 2 divisors :
119 &
17

119 ÷ 17 = 7 .
So, 119 is a multiple of 17.
Hence, RULE-1 CAN BE APPLIED.


Remainder for Greatest divisor (i.e.., 119) 'r' = 19.
Smallest divisor 'd' = 17.

19 > 17 => r > d
•°• Follow case-a of the rule


Divide 19 by 17

17 ) 19 ( 1
..……17
----------------
.……(2) = Required Remainder for smaller divisor ( i.e., 17).

•°• Required remainder = 2.


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Hope it helps.

Answer 2

Answer:

Step-by-step explanation:

Given :-

A number divided by 119 leaves as 19.

If the same number is divided by 17.

To Find :-

The Reminder.

Solution :-

Let, the Number = x  

Quotient = q  

Divisor = (d) = 119  

Remainder = (r) = 19  

X = (d x q) + r  

X = (119 x q) +19

Same number when divided by "17"  

x = (17 x 7 x q) + 17 + 2

= 17 (7q + 1) + 2  

Remainder is "2"

Hence, The remainder is 2.