Mathematics on HCF

Problem is given that there are four digit highest number , which when divided by 4,7,13 leaves the reminder 3 in each case


So we are to find out the common number
Four digit highest number is 9999

suppose we were given only one no say 4

we will divide   9999 by 4


 4  |   9999 | 2499
         8
___________
        1 9
____16_____
            39
             36
____________
               39
                36
           _____
                   3

For 4  , highest no is 9999 giving a remainder of  3

But the problem is with a sets of numbers 4,7,13

let us do the LCM of  4,7,13  which is  364

364 | 9999| 27    
         728
_________
           2719
           2548
__________
              171     Now remainder is  171 , if this remainder is diminished from the 9999 it will be exactly divisible

So     9999 - 171 = 9828

9828 is the four digit highest no. which is exactly divisible by the sets of numbers 4,7,13

But the problem does not end here , It is asking a number in which there will be a remainder of 3 .

So the required no will be  9828 +3 = 9831



Now another issues related to HCF and LCM of some numbers.

HCF is always a factor of the LCM that is LCM is divisible by the HCF

 Now there is a practical examples

The maximum no of students among them 1001 pens and 910 pencils can be distributed in such a way that each students get the same no of pens and pencil


This problem can be solved by simply doing the HCF of the numbers


HCF of this nos are 91

so the max no of students are 91 .