Question

Write all prime numbers between 1 and 10.

Answer 1

Hint: First of all try to recollect the definition of prime numbers and numbers which are not prime, that is composite numbers. Then recollect all the numbers which come under these categories. Then find out the numbers from 1 to 10 which come in under the category of prime numbers.


Complete step-by-step answer:
Here we have to write all the prime numbers between 1 to 10.
Before proceeding with this question, let us see what prime numbers and composite numbers mean.
Prime numbers: Prime numbers can be defined as the positive integers having only two factors, which are 1 and the integer itself. Let us consider an example, the factors of 6 are 1, 2, 3, and 6. We can see that there are four factors in total. But the factors of 5 are only 1 and 5. Hence, we can say that 5 is a prime number but 6 is not.

We can sum up and say that prime numbers are the numbers that are only divisible by 1 and the number itself.
Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc.
Composite numbers: Composite numbers can be defined as the positive integers that have factors other than 1 and the number itself. We can say that composite numbers are just the opposite of prime numbers. We can infer that any number which is not a prime number is composite. The smallest composite number is 4.
Some examples of composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 etc.
Also, the number 1 is not considered as prime or composite because the only factor it has in itself. As we have already seen, prime numbers have only 2 factors, 1 and itself. Composite numbers have more than 2 factors. 1 obeys neither of these rules because it has only 1 factor.

Now let us write all the prime numbers between 1 to 10.
First of all let us consider all the numbers from 1 to 10 that are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
Here, we already know that the number 1 is not considered as prime or composite.
Now, the numbers 2 and 3 are divisible only by 1 and itself, so both of them are prime numbers.
The number 4 has factors 1,2 and 4 which means it has more than two factors. So, it is a composite number.
The number 5 is divisible only by 1 and itself, so it is a prime number.
The number 6 has factors 1, 2, 3, and 6 which means it has more than two factors. So, it is a composite number.
The number 7 is divisible only by 1 and itself, so it is a prime number.
The number 8 has factors 1, 2, 4, and 8 which means it has more than two factors. So, it is a composite number.
The number 9 has factors 1, 3, and 9 which means it has more than two factors. So, it is a composite number.
The number 10 has factors 1, 2, 5, and 10 which means it has more than two factors. So, it is a composite number. Hence, we get a total of four prime numbers from 1 to 10 which are 2, 3, 5, and 7.

Note: Some students make this mistake of considering all the odd numbers as prime numbers but this is wrong. Numbers like 9, 15, 21, 25, etc. are odd but not prime numbers. Also, students must note that there is no defined formula to find if a number is prime or not, apart from finding its factors.