Question

What are all the prime factors of 144?

Answer 1

Hint: A factor that is prime in nature is said to be a prime factor of a number. In this question basically we need to find the prime numbers whose product gives the original and hence called the prime factors of a number nothing more than that.

Complete step-by-step answer:
Proceeding in this question we see that we need to find the prime factors of 144 which is actually a perfect square number and the number is 12.
We can therefore write the prime factor of 12 and then again write them in product since it is the square of a number 12.
So, the prime factors of 12 are 2,2,3 which gives us 4 $\times$ 3 and hence 12. So, the prime factors of 144 are 2,2,2,2,3,3.
Now, we should also remember that for any given number we can have only one set of prime factors. Therefore, we can say that prime factors of a number are unique in nature.
Hence, the prime factors of 144 are 2,2,2,2,3,3.

Note: Remember that 1 is neither composite nor prime. This condition is kept in order to preserve the uniqueness property of prime factors.
Prime factors are mainly used in divisibility, finding factors and making the common denominators.
Prime factors include repetition of numbers so do not be mistaken that every number is just written once and make the wrong set of prime factors.