Question

if we divide a number by 5, 6 and 3 the reminders are 2, 3 and 1 respectively if we reverse the number of dividers then what will be the reminders​

Answer 1

Given:

If we divide a number by 5, 6 and 3 the reminders are 2, 3 and 1 respectively.

To find:

The remainder if the numbers of the dividend is reversed.

Solution:

1) Let the number X divides with 5,6 and 3 leaves remainders are 2,3 and 1 respectively.

2) We will find the number X by the division algorithm, so the X is given by

• X = 5[6(3k+1)+3]+2

• X = 5[18k+6+3]+2

• X = 5[18k+9]+2

• X = 90k+45+2

• X = 90k+47

3) In the expression 90k+47 the 90k is completely divisible by 5,6 and 3 for any value of k so we will check for 47 only.

4) When the divisors are reversed

•    47/3 = 15 + remainder 2

•    15/6 = 3 + remainder 3

•    3/5  = 0 + remainder 3

The remainder if the numbers of the dividend is reversed are 2,3 and respectively.