Question

Find the greatest Value of A and B so that the following even number are divisible by both 3 and 5. (1)a2b (2) 2ab2a

Answer 1

a2b=a=4 , b=0
4*100+2*10+0=420

Answer 2

Answer:

(1)a=8 and b=5;

(2)a=5 and b=7

Step-by-step explanation:

We know that,

Any number is divisible by 3 if the sum of its digit is divisible by 3 and any number is divisible by 5 if its last digit is 0 or 5.

Part (1):

$a2b$

This number is divisible by 5 if b is taken as 0 or 5. Since we need the larger number so $b=5$.

Now we have the number $a25$

Now it is divisible by 3 if and only if

$a+2+5$ is divisible by 3.

$7+a$ is divisible by 3.

As we need the larger number, so we have $a=8$.

$a=8\;and\;b=5$

Part (2):

$2ab2a$

This number is divisible by 5 if a is taken as 0 or 5. Since we need the larger number so $a=5$

Now we have the number $25b25$

Now it is divisible by 3 if and only if

$2+5+b+2+5$ is divisible by 3.

$b+14$ is divisible by 3.

As we need the larger number, so we have $b=7$

$a=5\;and\;b=7$