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# Factors of 35 | Prime Factorization of 35

Number 35 is a composite number and we will find how to find the factors of 35 . We will also find out the Prime factorization of 35

### Factors of 35

A factor of a number is an exact divisor of that number. So factors of 35 are the number which are exact divisor of 35.
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 of 35

Method -1

Factors of 35 can be found by finding the numbers which when multiplied together gives the number 35.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
$35 = 1 \times 35$
$35 = 5 \times 7$
$35 = 7 \times 5$
We can stop here as 7 and 5 has occurred earlier.
So factors of 35 are 1,35,5,7

Method -2

Factors of 35 can be found by finding the numbers which divides the number without remainder . We can start with the following sequence 1,2,3,4… and go till the mid-point of that number
$35 /1 = 35$. No Remainder
$35/5 = 7$ . No Remainder
$35/7 = 5$. No remainder
$35/35=1$. No remainder.
So factors are 1,5,7,35

### Prime Factorization of 35

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

Now let us look on how to find the prime factorization of 35
There are two method which can be used.

Division method
We divide the number 35 by 2, 3, 5, 7 etc. in this order repeatedly so long
as the quotient is divisible by that number.Thus, the prime factorization of 100 is $3 \times 5$

Factor Tree Method
In this method, we first think about any two factor and then we think about two factors of respective number. This goes till the factors are prime.
We may have different factor tree depending on the starting point but all of them will show the same prime factors.
Lets check the different Factor tree for 35

### Factor of 35 in pair

We can find the factors of number 35 in pairs, by multiplying two numbers in a pair to get the original number as 35, such as:
$35 = 1 \times 35$
$35 = 5 \times 7$
So factor in pair are (1,35) & (5,7)

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