Question

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. Find out the number.

Answer 1

Let $p$ be the number.

Suppose,

$p÷4=q$, remainder$=2$

$q÷5=r$, remainder$=3$

$r÷6=s$, remainder$=4$

Then,

$r=6s+4$

$q=5r+3=5(6s+4)+3=30s+23$

$p=4q+2=4(30s+23)+2=120s+94$

Let us now assume that the remainder $s=1$. Then we have:

$p=(120\times 1)+94=214$

Hence, the number is $214$.