Question

Which of the following numbers has exactly 4 factors?
A. 16
B. 14
C. 18
D. None of these

Answer 1

Hint: According to the question, we have to find the number which has exactly 4 factors. So, first of all we have to check by option method.
Hence, first of all we have to use factor methods for each given option. So, first of all we have to understand about the factor method which is explained below.
Factor method: A common method of factoring numbers is to completely factor the number into positive prime factors. A prime number is a number whose only positive factors are 1 and itself. For example 2,3,5 and 7 are all examples of prime numbers.
Now, as we understand the factor method so first of all we have to find the factor of 16 by dividing it with the numbers 2,3,5 and 7 to check if there are four factors are possible or not.
Similarly, we have to find the factor of 14 by dividing it with the numbers 2,3,5 and 7 to check if four factors are possible or not.
Similarly, we have to find the factor of 18 by dividing it with the numbers 2,3,5 and 7 to check if four factors are possible or not.

Complete step-by-step answer:
Step 1: First of all we have to check option (A) by factor method that is explained in the solution hint.
Factors of $16 = 2 \times 2 \times 2 \times 2$
Hence, we have to see that the above number has exactly 4 factors that is $2 \times 2 \times 2 \times 2$.
Step 2: Now, first of all we have to check option (B) by factor method that is explained in the solution hint.
Factors of $14 = 2 \times 7$
Hence, we have to see that the above number has not exactly 4 factors that is $2 \times 7$.
Step 3: First of all we have to check option (C) by factor method that is explained in the solution hint.
Factors of $18 = 2 \times 3 \times 3$
Hence, we have to see that the above number has not exactly 4 factors that is $2 \times 3 \times 3$.

Hence, after checking by option by factor method we have to find that number 16 has exactly 4 factors. Hence, option (A) is correct.

Note:
To determine the factors of the given numbers we divide the given number first with the number 2 and then we have to divide it by 3 and same as with 5 and 7 until it is completely divisible.