Question

Find the greatest values of $a$ and $b$ so that the following even numbers are divisible by both $3$ and $5:$

$\left(i\right)a2b$

$i.e.,ax100+2x10+6$

$\left(ii\right)2ab2a$

$i.e.,10000x2+ax1000+bx100+2x10+a$

Answer 1

$\left(i\right)a2b$

Given, it is even number and divisible by both $3$ and $5.$

So, $b=0$

Also, $a+2$ must be divisible by $3$.

So, $a=1,4,7$

Out of $1,4,7$ greatest is $7$.

Hence, $a=7$ and $b=0$.

$\left(ii\right)2ab2a$

Given, it is even number and divisible by both 3 and 5.

So, $a=0$

Also, $4+b$ must be divisible by $3$.

So, $b=2,5,8$

Out of $2,5,8$ greatest is $8$.

Hence, $a=0$ and $b=8$.