Question

Explain why 1323343563715 is a composite number.

Answer 1

Hint: Here, we will use the divisibility tests of prime numbers 2, 3, 5, etc. to prove that the number 1323343563715 is a composite number. A composite number is a number which is not a prime number. It is divisible by more than 2 numbers (other than 1 and itself).

Complete step-by-step answer:
We will use the divisibility tests of prime numbers and prove that the number 1323343563715 is a composite number.
First, we will check the divisibility by 2.
We know that a number is divisible by 2 if it is an even number.
This means that any number that has one of the digits 2, 4, 6, 8, or 0 in the unit’s place, is divisible by 2.
We can observe that the number 1323343563715 has 5 at the unit’s place.
Therefore, the number 1323343563715 is not divisible by 2.
Next, we will check the divisibility by 3.
A number is said to be divisible by 3 only if the sum of its digits is divisible by 3.
We will add the digits of the number 1323343563715.
Thus, we get
\[1 + 3 + 2 + 3 + 3 + 4 + 3 + 5 + 6 + 3 + 7 + 1 + 5 = 46\]
Adding the digits of the number 46, we get
\[4 + 6 = 10\]
Since the number 10 is not divisible by 3, the number 46 is not divisible by 3.
Thus, the sum of the digits of the number 1323343563715 is not divisible by 3.
Therefore, the number 1323343563715 is not divisible by 3.
Next, we will check the divisibility by 5.
We know that a number is divisible by 5 if it has one of the digits 0 or 5 in the unit’s place.
We can observe that the number 1323343563715 has 5 at the unit’s place.
Therefore, the number 1323343563715 is divisible by 5.
Since the number is divisible by a number other than 1 and itself, it is not a prime number.
Therefore, the number 1323343563715 is a composite number because it is divisible by 5.

Note: We used the terms ‘prime number’ in the solution. A prime number is a number which is divisible only by 2 natural numbers, that is by 1 and the number itself. For example: 5 is a prime number because it is divisible by only 2 natural numbers, 1 and 5.