Question

3.
If 87587A28 is a number divisible by 8,
where A is a digit, how many such
numbers are possible?
(1) 5
(3)3
(2) 4
(4)9​

Answer 1

Given:

A number -

• 87587A28 which is divisible by 8.

What To Find:

We have to find -

• How many such numbers are possible to be divisible by 8 in the given options in place of A.

How To Find:

To find we have to -

• First, substitute each number given in the options in place of A.
• Next, use the divisibility rule of 8.
• Then, if the number is divisible we get an answer.
• Finally, we will get the possible number.

Divisibility Rule Of 8:

We take the 3 digits of the number and divide it by 8. There are two cases:-  

• If the remainder is 0 then it is divisible by 8.
• If the remainder is not 0 then it is not divisible by 8.

Solution:

Number - 87587A28

A. 5

Let's substitute it in the value of A.

→ A = 5

We will get -

→ 87587528

The three digits are -

→ 528

Divide it by 8,

→ 528 ÷ 8

The remainder is -

→ 0

∴ Hence, 87587528 is divisible by 8.

B. 3

Let's substitute it in the value of A.

→ A = 3

We will get -

→ 87587328

The three digits are -

→ 328

Divide it by 8,

→ 328 ÷ 8

The remainder is -

→ 0

∴ Hence, 87587328 is also divisible by 8.

C. 4

Let's substitute it in the value of A.

→ A = 4

We will get -

→ 87587428

The three digits are -

→ 428

Divide it by 8,

→ 428 ÷ 8

The remainder is -

→ 4

∴ Hence, 87587428 is not divisible by 8.

D. 9

Let's substitute it in the value of A.

→ A = 3

We will get -

→ 87587928

The three digits are -

→ 928

Divide it by 8,

→ 928 ÷ 8

The remainder is -

→ 0

∴ Hence, 87587928 is also divisible by 8.

Final Answer:

∴ Thus, the numbers possible are -

• 87587528 -- [5]

• 87587328 -- [3]

• 87587928 -- [9]