Question & Answer
QUESTION

How many numbers of prime factors does 36 have ?
A. 4
B. 3
C. 2
D. 1

ANSWER Verified Verified
Hint: Prime factors of any number are the factors of that number which are prime. So, we had to only split the given number into a product of its prime factors. And then count the number of factors.

Complete step-by-step answer:
As we know that prime numbers are those numbers which are only divisible by 1 and the number itself. But there is one exception that 1 is not the prime number.
As we know that factors of any natural number are the numbers by which that number is exactly divisible.
But prime factors are those factors of the number which are prime, and their product makes up the number itself.
So, now let us first find the factors of number 36.
As we know that 36 is divisible by 1, 2, 3, 4, 6, 9, 18. 36.
So, prime factors of 36 were { 1, 2, 3, 4, 6, 9, 18. 36 }.
But we are asked to find the number of prime factors of 36.
So, to split the number 36 into products of its prime factors we have to use prime factorization.

According to the prime factorization method we divide the number by the lowest prime number from which the number is divisible till we get a number equal to 1.
So, the lowest prime number is 2.
So, dividing 36 by 2. We get
\[\dfrac{{36}}{2} = 18\]
Now 18 is divisible by 2. So, dividing 18 by 2. We get,
\[\dfrac{{18}}{2} = 9\]
Now 9 is not divisible by 2. So, the next prime number is 3. So, dividing 9 by 3. We get,
\[\dfrac{9}{3} = 3\]
Now 3 is divisible by 3. So, on dividing 3 by 3 we get,
\[\dfrac{3}{3} = 1\]
So, the number 36 as the product of its prime factors is written as \[2 \times 2 \times 3 \times 3\].
So, prime factors of 36 are 2, 2, 3 and 3.
So, the total number of prime factors 36 had is equal to 4.
Hence, the correct option will be A.

Note: Whenever we come up with this type of problem then we have to write the given number as the product of prime factors. So, to do this we divide the number by the lowest prime number from which the number is divisible till we get the number equal to 1. After that we count the number of prime factors whose product is equal to the given number to get the required answer. And this will be the easiest and efficient way to find the solution of the problem.