Question

Is \[69\] a prime number?

Answer 1

Hint: We use the concepts of prime numbers and definitions of prime numbers to solve this problem. We also use divisibility rules to solve this problem. We will look at some examples of prime numbers and also some examples of numbers which are not prime numbers.

Complete step by step answer:
A prime number is a natural number greater than 1, which is divisible only by 1 and the number itself.
So, in other words, numbers which have only two divisors have been called prime numbers.
All other numbers other than prime numbers are called composite numbers.
For example, take the natural number 2.
So, the number 2 is only divisible by two numbers which are 1 and 2. So, 2 is a prime number.
Take another example 5, which is also having two divisors 1 and 5. So, 5 is also a prime number.
These are the few prime numbers:
\[2,3,5,7,11,13,17,19,23,29,31,......\]
Every composite number can be written as a product of prime numbers.
For example, take number 24, which is a composite number.
So, we can write 24 as, \[24 = 2 \times 2 \times 2 \times 3\]
Now, consider the number 69.
Recall the divisibility rule of 3. If the sum of digits of a number is a multiple of three, then that number is divisible by 3.
So, in number 69, \[6 + 9 = 15\] which is a multiple by 3.
So, 69 is divisible by 3. And also, it is divisible by 1 and 69 too.
The divisors of 69 are \[1,3,23,69\].
So, the number 69 has more than two divisors. So, 69 is NOT a prime number.

Note:
The number 1 is neither a prime number nor a composite number. And the number 2 is the least prime number. If a number has an even number as its last digit, then it is divisible by 2. This is the divisibility rule of 2.
Also remember that two prime numbers with a difference 2, are called twin primes.
For example, \[(3,5)\] and \[(11,13)\]