Factors of 75 /How to Find Prime Factors , Prime Factorization and Factor Pairs of 75?

•Positive factors of 75 are: 1,3,5,15, 25 and 75.

•Negative factors of 75 are: -1,-3,-5,-15, -25 and -75.

•75 has 6 factor pairs which are:

(1×75),( 3× 25), (5 ×15),

(-1×-75), (-3× -25),( -5 ×-15).

•Prime factors of 75 are: 3,5

•Prime Factorisation of 75 is: 3×5×5 or, 3×5²

Explanation:

Today we are going to find out the factors of 75 in just few steps.

              Step-1:

◆The numbers that can divide 75 without remainder are called 75's factors.

◆Rule-1: N's factor is the number that can divide N without remainder.

◆Notice that the factors always includes 1 and itself.

            Step-2:

Notice that the factors always includes 1 and itself.

So,the factors of 75 are 1, ............75.


●A simple way is to find what pairs of numbers multiply to get 75.


●75=1×75

75 is divisible by 1 and 75 without any remainder.So,1 and 75 are the two factors of 75.

Proofs:

●75/1=75

●75/75=1


             Step-3:

Already we have gotten two factors of 75 which are 1 and 75.In this step we will find out other factors of 75 by applying the following rule.



◆N's factor is the number that can divide N without remainder.


So,the numbers that can divide 75 without remainder are called 75's factors.


●A simple way is to find what pairs of numbers multiply to get 75.





75=3×25


75=5×15




Proofs:


●75/3=25

●75/25=3

●75/5=15

●75/15=5



75 is divisible by 25,3,15,5 without any remainder.


So,the total number of positive factors of 75 (including 1 and itself) are 1,3,5,15, 25 and 75.
 

            Step-4:

●We have to keep in mind that the factors of an integer include both the positive and negative integers.


So, the factors of 75  include negative numbers or integers. Hence, all the positive factors of 75 can be easily converted to negative numbers .The negative factors of 75 are given below:

-1,-3,-5,-15, -25 and -75.


Look carefully:

(◆Negative times  Negative=Positive) 


75= -1 × -75


75= -3 × -25


75= -5 × -15


So,the total number of  negative factors of 75  are --1,-3,-5,-15, -25 and -75.

●How many factors does the number 75 have?

Ans:75 has 12 factors totally.The number 75 has 6 positive factors and 6 negative factors.





◆Factor Pairs of 75

Here are the factor of pairs of 75.

●A simple way is to find what pairs of numbers multiply to get 75.



◆75=1×75


●75=3×25


●75=5×15

Look carefully:

(◆Negative times  Negative=Positive) 

◆75= -1×-75


●75= -3×-25


●75= -5×-15

The integer 75 has 6 factor pairs.These are given below:
1×75,3× 25,5 ×15,

-1×-75,-3× -25,-5 ×-15.

•Prime Factorization of 75

Now we are going find out the prime factorization of 75 by using factor tree method.

From above picture,3 and 5 are the prime factors of 75.Besides,3×5^2 is the prime factorization of 75.