Question

3 digit number with which 43259 must be multiplied ,so that the product ends with 437 is

Answer 1

Answer:

743

Step-by-step explanation:

Let the 3 digit number be 'xyz'

We should get product ending with 437 hen 43259 is multiplied by xyz,

=>(43000+259)*xyz

It is clear that last 3 digits depend only on product 259*xyz

last digit  of the product= 9 multiplied by z should end in 7, this happens only if z =3.

Hence 3digit number is xy3.

Counting number of 10's.

Now, counting number of 10's  in 259*xy3,

= last digit in 25*3 + xy*9 +2(carry from 9*3)

=last digit in xy*9 + 77 should be 3

=> xy*9 should end in 6

this is possible only if y =4.

Hence 3digit number is of form x43.

Counting number of 100's in 259*x43

=259*(x00+43)

=last digit in 259*x + number of hundreds in 259*43

We can calculate and observe that number of hundreds in 259*43 are 111

, so 111+last digit in 259*x should end with 4

=>last digit in 259*x should end in 3

This would be possible only if x is 7.

Hence 'xyz' = 743.