Question

If one number is divided by 345 the remainder is 35 if the same number is divided by 15 what is the rem
ainder

Answer 1

let the number be "x"

the number "x" is divided by "345" and we get remainder as "35" , hence we can write

x = 345 y + 35                     where y = integer

rearranging the expression so that we have "15" in multiple

x = (23 x 15) y + 30 + 5

x = (23 x 15) y + (15 x 2) + 5

x = 15 (23 y + 2) + 5

hence dividing the number by "15" , we get remainder "5"

Answer 2

Solution 1:

Let N=345×q+35

=15(23q)+15×2+5.

So the remainder will be 5

Solution 2:

Let that one number is x

then x=345×a+35  

now 345÷15=23 , ie 23×15=345

So, x=15×23×a+35 =15×23×a+15×2+5

=15(23×a+2)+5

Then x will be divided by 15

The remainder will be 5