factors-of-9
Factors of 9

What are the factors of 9?

Factors of 9: 1, 3, 9
Negative factors: -1, -3, -9
Pairs of factors: 1×9, 3×3 
Prime factors: 3, 3
Number of positive factors: 3
Number of Negative factors: 3
A total number of factors = 6

Definition of factors in math

Multiplying two whole numbers to get the original/product number and a whole number that divides exactly into another number that is called factoring.


Factors of 9 in pairs

Factors of 9 are- 1×9 = 9, 3×3 = 9, as you can see we have multiplied two whole numbers with a combination of factors which gives the original/product number (9) in the result.
We can find the Factors of 9 by multiplying two whole numbers in a pair to get the result 9.

factors-of-9
Multiply by (1)       1 × 9 = 9
Multiply by (3)       3 × 3 = 9

 There are no more possible pairs so we have all the factors in question.
Factors pairs of 9 = (1×9) (3×3) 
Add all these to our factors list
Factors list: -



Prime Factorization of 9 :-

Step 1: - We can divide the given number (9) by the smallest prime number that divides the number exactly.
We can easily divide 9 by the smallest prime number 3.
 9/3 = 3

Step 2: - Divide the quotient again by the smallest or the next smallest prime number. We will repeat this process repeatedly until the quotient becomes 1.
9 ÷ 3 = 3
3 ÷ 3 = 1

 Prime factors are: -
3, 3
Multiply all prime factors
3 × 3 = 9

Multiples of 9: - 

9   ×   1   =   9
9   ×   2   =   18
9   ×   3   =   27
9   ×   4   =   36
9   ×   5   =   45
9   ×   6   =   54
9   ×   7   =   63
9   ×   8   =   72
9   ×   9   =   81
9   ×   10   =   90

How many factors of 9? 

9 has (3) Factors (1, 3, 9) and 6 with negative Factors (-1, -3 and -9).



How many odd and even factors of 9?

9 has (3) odd factors (1, 3, 9) and (0) even factors.

How to find the number of odd factors?

Step 1: -  At, first find the prime factorization of given number.
 9 = 3 * 3

Step 2: - Express them into exponential form.
3 * 3 = 3^2

Step 3: - To find the number of odd factors you always have to write the exponent (1) in the base of 2. But in this case you do not have two (2) so leave it and then add (+1) in all the other exponents.
3^2+1 = 3^3

Step 4: - Leave the base and multiply all exponents.
Exponent 3 = 3

Answer. The total number of odd factors is = 3


How to find the sum of odd factors?

The first two steps are the same, factorization of the given number and expressing them in to exponential form.
9 = 3 * 3
3 * 3 = 3^2

If you want to find the sum of odd factors, you always have to write (0) in the exponent of 2. But in this case you do not have 2 so leave it. And besides them start all bases of the exponent from (0) and move up to maximum power of base and solve them.
3^0 + 3^1 + 3^2
1 + 3 + 9 = 13

Answer. The sum of odd factors is 13.

Odd factors of 9
1, 3, 9, 
Sum of odd factors
1 + 3 + 9 + = 13

Even factors of 9
= 0
Sum of even factors
= 0

How to find the total number of factors?

Step 1: - At, first find the prime factorization of given number.
9 = 3 * 3

Step 2: - Express them into exponential form
3 * 3 = 3^2

Step 3: - Leave the base (3) and raise all exponent by (+1) one.
2+1 = 3

Answer: Total number of factors is 3.

How to find the sum of total factors?

The first two steps are the same, factorization of the given number and expressing them in to exponential form.
9 = 3 * 3
3 * 3 = 3^2

Start all bases of the exponent from (0) and move up to the maximum power of base and solve them.
3^0 + 3^1 + 3^2
1 + 3 + 9 = 13

Answer. The sum of total factors is 13

All factors of 9
1, 3, 9
Sum of all factors
1 + 3 + 9 = 13
Some more questions: -

 Is 9 a composite number?
Yes! 9 is a composite number.

 Is 9 a prime number?
No! 9 is not a prime number.

 Is 9 a perfect square?
Yes! 9 is a perfect square.(9) is a square root of 3.

 Is 9 an even number?
No! 9 is not an even number.

 Is 9 an odd number?
Yes! 9 is an odd number.

Is 9 a rational number?
Yes! 9 is a rational number.

 Is 9 a irrational number?
No! 9 is not an irrational number.



Last words: - I hope this step-by-step tutorial was useful to teach you about the Factors of 9. Do you want to learn something else? So always come back to our site.
Thank you.