Factors of 9
Factors | Factor Pairs | Prime Factorization |
|---|---|---|
1, 3, 9 | (1, 9), (3, 3) | 3 x 3 |
What are the Factors of 9?
The factors of 9 are natural numbers that divide 9 without leaving any remainder, or in other words, factors of 9 divide 9 evenly.
Example: 3 is a factor of 9 because when we divide 9 by 3, it gives us the quotient as 3 and the remainder as 0.
So, to check if any number is a factor of 9 or not, divide 9 by that number and verify whether the remainder is zero or not. If the remainder is zero then the number is a factor of 9 otherwise not.
[Note: When a number is divided by its factor the quotient obtained is also a factor of the number.]
Factor List of 9
Factors of 9 can be obtained by applying the divisibility rules and division facts.
We can stop checking after 8 as the factor pairs start to repeat.
So the factors of 9 are 1, 3 and 9.
Prime Factors of 9
The prime factorization of a number expresses the number as the product of prime numbers. Here the prime numbers multiplied are known as the prime factors of the original number.
A factor tree can be used to learn about the prime factorization of 9.
From the factor tree we can see prime factorization of 9 is 3 × 3 = 3\(^2\).
This means, 3 is the only prime factor of 9.
Read More:
Factor Pairs of 9
The factor pair of 9 is the combination of two factors of 9 which when multiplied together result in 9.
Example: (1, 9) is a factor pair of 9 as 1 x 9 = 9
A factor pair can be a positive pair or a negative pair.
The factor pairs of a number can be written from the list of factors of that number.
Positive Factor Pairs of 9
Positive factor of 9 | Positive Factor Pairs of 9 |
|---|---|
1 × 9 | (1, 9) |
3 × 3 | (3, 3) |
So the positive factor pairs of 9 are (1, 9) and (3, 3).
Rapid Recall
Solved Factors of 9 Examples
Example 1: Find the common factors of 12 and 9.
Solution:
Factors of 12: 1, 2, 3, 4 , 6 and 12.
Factors of 9: 1, 3 and 9.
So, the common factors of 12 and 9 are 1 and 3.
Example 2: Find the greatest common factor of 9 and 81.
Solution:
Factors of 9: 1, 3 and 9.
Factors of 81: 1, 3, 9, 27 and 81.
So, the common factors of 9 and 81 are 1, 3 and 9.
Therefore the greatest common factor of 9 and 81 is 9.
Example 3: You need 9 balloons for a small party. Balloons come in packs of 2, 3 and 5. Which pack will you buy so that all the balloons are used for the party?
Solution:
Total number of balloons = 9
Out of 2, 3 and 5 only 3 is a factor of 9, that is, 9 is evenly divisible by 3.
So you need to buy 3 packs of 3 balloons so that all the 9 balloons are used for the party.
When you divide 9 by 2 it will give 1 as a remainder, that is, 2 does not divide 9 evenly. So 2 is not a factor of 9.
9 has three factors, that is, 1, 3 and 9. So it is not a prime number.
The natural numbers 1, 3 and 9 divide 9 evenly.
We know 3 x 3 = 9 so square root of 9 = 3 which is a whole number. So 9 is a perfect square.
The factors of 9 are 1, 3 and 9.
So, the least factor of 9 is 1, and the greatest factor is 9 itself.