Question

How many composite numbers are there in between 150 and 200 (including 150 and 200 both)?
A. 40
B. 42
C. 41
D. 39
E. None of these

Answer 1

Hint: Before attempting this question, you must have prior knowledge of composite number is must, and you should know the factors of numbers between 150 and 200 including (150 and 200), use this information to approach toward the solution of the question.

Complete step-by-step answer:
We have to find the composite numbers between 150 and 200 including (150 and 200) and to do so first we have to find the numbers present between them and the nature and factors of them
So the numbers between 150 to 200 (including 150 and 200) are 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199 and 200
In the above series of numbers let’s differentiate the even numbers and odd numbers
Even numbers are 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198 and 200
Odd numbers are 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, and 199
Since we know that every even number accept 2 have more at least 1 factors accept 1 and itself
Since not every odd number have factors more than 2 let’s find out the factors of the given numbers
Factors of 151 are 1, 151 so it is not a composite number
Factor of 153 are 1, 3, 9, 17, 51 and 153 so it is a composite number
Factor of 155 are 1, 5, 31 and 155 so it is a composite number
Factor of 157 are 1 and 157 so it is not a composite number
Factor of 159 are 1, 3, 53 and 159 so it is a composite number
Factors of 161 are 1, 7, 23 and 161 so it is a composite number
Factors of 163 are 1 and 163 so it is not a composite number
Factors of 165 are 1, 3, 5, 11, 15, 33, 55 and 165 so it is a composite number
Factors of 167 are 1 and 167 so it is not a composite number
Factors of 169 are 1, 13 and 169 so it is a composite number
Factors of 171 are 1, 3, 9, 19, 57 and 171 so it is a composite number
Factors of 173 are 1 and 173 so it is not a composite number
Factors of 175 are 1, 5, 7, 25, 35 and 175 so it is a composite number
Factors of 177 are 1, 3, 59 and 177 so it is a composite number
Factors of 179 are 1 and 179 so it is not a composite number
Factors of 181 are 1 and 181 so it is not a composite number
Factors of 183 are 1, 3, 61 and 183 so it is a composite number
Factors of 185 are 1, 5, 37 and 185 so it is a composite number
Factors of 187 are 1, 11, 17 and 187 so it is a composite number
Factors of 189 are 1, 3, 7, 9, 21, 27, 63 and 189 so it is a composite number
Factors of 191 are 1 and 191 so it is not a composite number
Factors of 193 are 1 and 193 so it is not a composite number
Factors of 195 are 1, 3, 5, 13, 15, 39, 65 and 195 so it is a composite number
Factors of 197 are 1 and 197 so it is not a composite number
Factors of 199 are 1 and 199 so it is not a composite number
So we have total 26 even numbers which are composite numbers and 25 odd numbers form which 14 numbers are composite number and 11 are non-composite numbers
So the total numbers of composite numbers are 26 + 14 = 40 numbers
Hence option A is the correct option.

Note: The concept of composite number which we used in the above solution can be explained as the number which is the multiple of 2 or more than 2 integers such that it has at least 1 divisor excluding number 1 and the number itself. These numbers which are the divisor of the number are named as the factors of number example of composite number are even numbers accept 2 and non-prime numbers.