Question

What are the prime factors of $20$?

Answer 1

Hint: In order to find the prime factors of $20$, it's important to know the difference between factors and prime factors. Factors of any number are the numbers that produce the same number as result when a pair of its factors are multiplied. Whereas, prime numbers are numbers which are divisible by two numbers only, first is one and second is the number itself.

Complete step by step solution:
We are given a number $20$.
From the definition of factors, we know that the factors are the numbers which when multiplied with other factors of the same number, then the original number should be obtained.
Factors can be any positive and negative numbers.
So, for $20$, we need to find the values which can divide it completely and give zero as remainder.
From this theorem, we get that the factors of $20$ between $1$ to $20$ are $1,2,4,5,10,20$.
But we are given to find the prime factors of the number, and we know that prime number means the numbers which cannot be divided by any number except the number $1$ and the number itself.
Since, the number $1$ is neither prime nor composite, so that number would be excluded.
Now, from the factors list of $20$, we can see that there are only two numbers which are not further divisible (except $1$) and that is $2$ and $5$. Which means they are prime numbers and also, they are factors of $20$. Together they become the prime factors of the number.

Therefore, the Prime factors of $20$ are $2$ and $5$.

Note:
1) Similarly, the factors can be in the negative part also because when two negative factors multiplied, they would give the original positive number that is $20$, so the factors can be $ - 1, - 2, - 4, - 5, - 10, - 20$. And, these are called the negative prime factors of the number.
2) We can also use the prime factorization method to find the prime factors of the number.