Answer
Verified
450.3k+ views
Hint: We know that a number is a prime number when it has two positive divisors i.e. 1 and itself and a number is a composite number when it has more than two positive divisors and at least one of the divisors is not 1 and itself. Now, check the options given in the question which are neither prime nor composite.
Complete step-by-step answer:
We are asked to find the option which is neither prime nor composite. We know that a prime number is a number which has only two positive divisors i.e. 1 and itself.
A composite number is a number which has at least one its divisors not 1 or the number itself,
Now, we are going to check the options given in the above problem whether they are neither prime nor composite.
Checking option (a) 0 we get,
0 is not a prime number because there are infinite factors which we multiply by 0 gives 0 so the definition of prime number which has only two factors 1 and itself is not satisfying.
0 is not a composite number because it is not a positive integer which is not satisfying the fundamental arithmetic and 0 cannot be divided by itself then we will get $\dfrac{0}{0}$ which is an indeterminate form.
Hence, 0 is neither prime nor composite.
Hence, option (a) is correct.
Checking option (b) 1 we get,
1 is not a prime number because for a prime number the number should have two divisors 1 and itself. Now, 1 has only one divisor i.e. 1.
1 is not a composite number because a number to a composite number when it has a divisor which is not 1 and itself so here 1 has only one divisor i.e. 1.
Hence, 1 is neither a prime nor a composite number.
Hence, option (b) is correct.
Checking option (c) 2 we get,
2 is a prime number because it has two positive divisors 1 and 2 which is satisfying the definition of a prime number.
2 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 2 is a prime number but not a composite number.
Checking option (d) 5 we get,
5 is a prime number because it has two positive divisors 1 and 5 which is satisfying the definition of a prime number.
5 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 5 is a prime number but not a composite number.
From the above options, the correct option is (a) and (b).
Note: You might think 0 is a composite number because it has an infinite number of factors which on multiplication by 0 will give 0 but here 0 cannot be divisible by itself that’s why 0 is not a composite number.
You also might think that 1 is a prime number as if we multiply 1 by itself we get 1. But as you can see that the divisor 1 is creating ambiguity here like whether 1 is the number itself or the number 1 so 1 is not a prime number.
Complete step-by-step answer:
We are asked to find the option which is neither prime nor composite. We know that a prime number is a number which has only two positive divisors i.e. 1 and itself.
A composite number is a number which has at least one its divisors not 1 or the number itself,
Now, we are going to check the options given in the above problem whether they are neither prime nor composite.
Checking option (a) 0 we get,
0 is not a prime number because there are infinite factors which we multiply by 0 gives 0 so the definition of prime number which has only two factors 1 and itself is not satisfying.
0 is not a composite number because it is not a positive integer which is not satisfying the fundamental arithmetic and 0 cannot be divided by itself then we will get $\dfrac{0}{0}$ which is an indeterminate form.
Hence, 0 is neither prime nor composite.
Hence, option (a) is correct.
Checking option (b) 1 we get,
1 is not a prime number because for a prime number the number should have two divisors 1 and itself. Now, 1 has only one divisor i.e. 1.
1 is not a composite number because a number to a composite number when it has a divisor which is not 1 and itself so here 1 has only one divisor i.e. 1.
Hence, 1 is neither a prime nor a composite number.
Hence, option (b) is correct.
Checking option (c) 2 we get,
2 is a prime number because it has two positive divisors 1 and 2 which is satisfying the definition of a prime number.
2 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 2 is a prime number but not a composite number.
Checking option (d) 5 we get,
5 is a prime number because it has two positive divisors 1 and 5 which is satisfying the definition of a prime number.
5 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 5 is a prime number but not a composite number.
From the above options, the correct option is (a) and (b).
Note: You might think 0 is a composite number because it has an infinite number of factors which on multiplication by 0 will give 0 but here 0 cannot be divisible by itself that’s why 0 is not a composite number.
You also might think that 1 is a prime number as if we multiply 1 by itself we get 1. But as you can see that the divisor 1 is creating ambiguity here like whether 1 is the number itself or the number 1 so 1 is not a prime number.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Write a letter to the principal requesting him to grant class 10 english CBSE