Think of a 135 digit number formed by writing the first 72 natural number side by side in a string.(i.e.) 1 2 3………70 71 72. Find the remainder when it is divided by 12.

a. 2
b. 9
c. 0
d. 5

its B

how

explain

To find the remainder when the number formed by writing the first 72 natural numbers side by side is divided by 12, we can use the concept of divisibility rules.

The divisibility rule for 12 states that a number is divisible by 12 if it is divisible by both 3 and 4.

First, we check if the number formed by writing the first 72 natural numbers is divisible by 3. We can do this by summing up the digits and checking if the sum is divisible by 3.

To get the sum of the digits, we need to find the sum of the first 72 natural numbers. We can use the formula for the sum of an arithmetic series:

Sn = (n/2) * (a + l)

Where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

Plugging in the values, we get:

Sn = (72/2) * (1 + 72)
= 36 * (1 + 72)
= 36 * 73
= 2628

Now we need to find the sum of the digits in 2628. We can do this by repeatedly summing the digits until we get a single-digit number.

2 + 6 + 2 + 8 = 18
1 + 8 = 9

Since 9 is divisible by 3, we can conclude that the number formed by writing the first 72 natural numbers is divisible by 3.

Next, we need to check if the number is divisible by 4. A number is divisible by 4 if the last two digits are divisible by 4. In this case, the last two digits are 72.

Since 72 is divisible by 4, we can conclude that the number formed by writing the first 72 natural numbers is divisible by 4.

Therefore, since the number is divisible by both 3 and 4, it is also divisible by 12. This means that the remainder when it is divided by 12 is 0.

Therefore, the correct answer is c. 0.