Question

A seven digit number a412bc5 is given. Find the no. of possible values of (a,b,c) such that the given seven digit number is divisible by 375. Answer and take take ten points

Answer 1

Step-by-step explanation:

Given -

• a412bc5

To Find -

• Value of a, b, c such that given seven digit number is divisible by 375

375 = 125 × 3

It is cleared that,

The given number is divisible by 125 and 3

As we know that :-

If a number is divisible by 125 its last three digit must be a multiple of 125 i.e, 125, 250, 375, 500

And

here the last digit is given 5

Now, it is cleared that

The last three digit must be 375

And

As we know that :-

If a number is divisible by 3 then the sum of the numbers must be divisible by 3.

It means,

a + 4 + 1 + 2 + b + c + 5 is divisible by 3

Now,

• Last three digit number is 375

Then,

b = 3

c = 7

Then,

a + 4 + 1 + 2 + 3 + 7 + 5 is divisible by 3

» a + 22 is divisible by 3

Then,

The value of a must be 2 Because if we put a = 2 then the number comes is 24 and it is divisible by 3

Hence,

The value of

a = 2

b = 3

c = 7

Answer 2

The value of

• a = 2
• b = 3
• c = 7

Step-by-step explanation:

Given :

A seven digit number : a412bc5

To Find :

The value of a, b, c such that given seven digit number is divisible by 375.

Solution :

It is given that,

The given seven digit is divisible by 375.

So,

The number 375 is divisible by 125 & 3.

We learned that,

If an amount is divisible by 125 its last three digit must be a multiple of 125 .

Hence,

$\bf \implies a + 4 + 1 + 2 + b + c + 5\qquad\bigg[Divisible\;by\;3\bigg]$

The last digit is given 5.

So,

The values of :

• b = 3
• c = 7

$\implies \sf a + 4 + 1 + 2 + 3 + 7 + 5\qquad\bigg[\bf Divisible\;by\;3\bigg]\\ \\ \\\implies \sf a + 22 \qquad\bigg[\bf Divisible\;by\;3\bigg]$

Now, if you put a = 2.

⇒ 2 + 22

⇒ 24

The number 24 is divisible by 3.

Hence,

The value of

• a = 2
• b = 3
• c = 7