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# Factors of 75 | Prime Factorization of 75

Number 75 is a composite number and we will find how to find the factors of 75. We will also see techniques to find out the Prime factorization of 75 easily

### Factors of 75

A factor of a number is an exact divisor of that number. So factors of 75 are the number which is an exact divisor of 75.
Factors of any number can be found by finding the number which divides the number without remainder or alternatively numbers that can multiply together to equal the target number being converted

Let us check how to find the factors

Method -1

Factors can be found by finding the numbers which when multiplied together gives the number 75. Now to find the numbers we can start with integer 1 and keep increasing it by 1 and we will discard where the other number cannot be found. We will stop at a point where we start seeing the repetition of numbers We will find the multiplication one by one and start writing down. So
$75 = 1 \times 75$
$75 = 3 \times 25$
$75 = 5 \times 15$
$75 = 15 \times 5$
We can stop here as 15 and 5 have occurred earlier.
So factors are 1,75,3,25,5,15

Method -2

Factors can be found by finding the numbers which divide the number without a remainder. We can start with the following sequence 1,2,3,4… and go till the mid-point of that number
$75 /1 = 75$. No Remainder
$75/3 = 25$ . No Remainder
$75/5 = 15$. No remainder
$75/15=5$. No remainder.
$75/25=3$. No remainder.
So factors are 1,3,5,15,25,75

Hence Factors of 75 are 1,3,5,15,25,75

### Prime Factorization of 75

When a number is expressed as a product of its factors we say that the number has been factorized. When the factorization contains the prime number only then it is called prime factorization.

Now let us look at how to find the prime factorization
There are two methods that can be used.

Division method
We divide the number 75 by 2, 3, 5, 7, etc. in this order repeatedly so long
as the quotient is divisible by that number.Thus, the prime factorization is $3 \times 5 \times 5$ or $3 \times 5^2$

Factor Tree Method
In this method, we first think about any two factors and then we think about two factors of respective number. This goes till the factors are prime.
We can have many factor trees depending on the starting point but all of them will show the same prime factors.
Let’s check the different Factor trees for number 75

Hence the Prime Factorization is $3 \times 5^2$

### Factor of 75 in pair

We can find the factors of number 75 in pairs, by multiplying two numbers in a pair to get the original number as 75, such as:
$75 = 1 \times 75$
$75 = 5 \times 15$
$75 = 3 \times 25$
So factor in pair are (1,75) , (5,15) and (3,25)

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