Question

How do you find the prime factorization of $75?$

Answer 1

Hint: Whenever they ask to find prime factors of any given number we need to find the factors of a number which are prime numbers. By using a simple division method in which the remainder should be zero to consider it as one of the factors, we can get the prime factors of a given number.

Complete step-by-step answer:
Here they have asked for prime factors of the number $75$ .
Before finding the prime factors first we need to know what are factors and the difference between factor and a prime factor.
Factors are nothing but the number which divides the given number with zero as the remainder.
Prime factors also refers to the factors but here the number which divides the given number should be the prime number. Prime numbers are nothing but the number which are divisible only by $1$ and the number itself. Therefore starting some of the prime numbers are: $2,3,5,7,11,13,1,19,23,29$ and so on.
So now, we check from the starting prime number so that we get the required prime factors of $75$.
First we take $2$, it does not divide the number with zero remainder so this is not the prime factor.
Now we check for the next prime number that is $3$. We get
$\dfrac{{75}}{3} = 25$ with zero remainder.
Now if we divide $25$ by $3$ we get a fractional number which can’t be a factor. So we check for the next prime number that is $5$.
Therefore, we get
$\dfrac{{25}}{5} = 5$
Again we can divide $5$ by $5$, we get
$\dfrac{5}{5} = 1$
Now, at the end of the division process we got number one which cannot be divided further. So the prime factors of the number $75$ are $3,5,5$ .

Note: Whenever they ask for prime factors the factor number should be prime number. The factors of any number can be a prime factor, but all the factors can not be prime factors. In the other word we can say all the prime factors can be factors but all the factors can not be prime factors.