Factors of 9 are the list of integers that we can split evenly into 9. It has a total of 3 factors of which 9 is the biggest factor and the positive factors of 9 are 1, 3 and 9. The sum of all factors of 9 is 13 and its factors in Pairs are (1, 9) and (3, 3).
- Factors of 9: 1, 3 and 9
- Negative Factors of 9: -1, -3 and -9
- Prime Factors of 9: 3
- Prime Factorization of 9: 3 × 3 = 32
- Sum of Factors of 9: 13
| 1. | What are Factors of 9? |
| 2. | How to Calculate the Factors of 9? |
| 3. | Factors of 9 by Prime Factorization |
| 4. | Factors of 9 in Pairs |
| 5. | Important Notes |
| 6. | FAQs on Factors of 9 |
What are Factors of 9?
When we divide 9 by 3, it is exactly divisible and leaves no remainder which means that 3 is a factor of 9. Note that 1 and the number itself are always factors of the number. Thus, the factors of 9 are 1, 3, and 9.
How to Calculate the Factors of 9?
Factors of 9 can be calculated by the division method. In the division method, we find the numbers which divide 9 exactly without leaving a remainder.
Factors of 9 by Division Method
For finding the prime factors of 9 by division method, we should divide 9 by natural numbers and see which numbers exactly divide 9 and give 0 as the remainder.
- Step 1: When we divide 9 by 1, 3, and 9, the remainder will be 0.
- Step 2: At the same time, when we divide 9 by numbers like 2 or 4, it leaves a remainder.
- Step 3: Try to divide 9 by the above numbers and see the results.
Therefore, the factors of 9 are 1, 3, and 9. Explore factors using illustrations and interactive examples:
- Factors of 69: The factors of 69 are 1, 3, 23, 69.
- Factors of 49 - The factors of 49 are 1, 7, 49.
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
- Factors of 119 - The factors of 119 are 1, 7, 17, 119.
- Factors of 91 - The factors of 91 are 1, 7 13, 91.
- Factors of 900 - The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900.
Factors of 9 by Prime Factorization
In the prime factorization method, we divide 9 by prime numbers and see if it does not leave any remainder. We then continue division with the quotient. In this way, 9 is expressed as a product of its prime factors. We can find the prime factors by the division method or factor tree method.
Prime Factorization of 9 by Division Method
The number 9 is divided by the smallest prime number which divides 9 exactly. The quotient thus obtained is then divided by the smallest or second smallest prime number and the process continues till the quotient is equal to 1.
- Let us divide 9 by the prime number 3, 9 ÷ 3 = 3
- Since 3 is the smallest odd prime number, it cannot be further divided.
- Thus, the factors of 9 are 3 and 9.
Prime factorization of 9 is 9 = 3 × 3.
Prime Factorization of 9 by Factor Tree Method
We have to find the prime factors of 9, therefore, the root of our factor tree is 9. We have to write a pair of factors as a branch of 9.
Let us see how a factor tree of 9 looks like:
Here, 3 is a prime factor. Thus, the factor tree ends here. Therefore, the prime factorization of 9 is 3 × 3.
Prime Factorization of 9 by Upside Down Division Method
This method is called the upside-down division method because the division symbol is flipped upside down. Here, we divide 9 by the smallest prime number, that is, 3. If the given number is even, we divide by 2.
We know that 3 is the smallest odd prime number, hence, it cannot be further divided. Therefore, 9 can be expressed as 3 × 3.
Factors of 9 in Pairs
Pair factors refer to the set of two numbers which when multiplied give the number as the product. Pair factors of 9 are:
- 1 × 9 = 9
- 3 × 3 = 9
There can be negative pair factors for 9 as well. They are (-1, -9) and (-3, -3).
Important Notes:
- Factors of 9 are 1, 3, and 9.
- 1 is a universal factor.
- Factors of a number are the numbers we multiply to get that particular number.
Factors of 9 Solved Examples
Example 1: Three students have 9 minutes to speak about a particular topic during a competition. The time given to each one of them to speak is split among them equally. How much time will each one of them get?
Solution:
There are 3 students and 9 minutes. To divide the time equally among them, we need to determine the factor of 9 which will divide the time equally among the 3 students.
Hence, we divide 9 by 3. 9 ÷ 3 = 3.
Since 3 is a factor of 9, when 3 is multiplied by 3, it gives 9.
Therefore, each student will get 3 minutes to speak about the topic.
Example 2: Nick was playing a math game with his friends. In the game, he was asked to find the factors of 9. What will be his answer?
Solution:
9 is a composite number. Therefore the factors of 9 are 1, 3, and 9.
Example 3: Ross is calculating the sum of all the factors of 9. Can you help him find the sum?
Solution:
We know, the factors of 9 = 1, 3, 9. Thus, the sum of all the factors = 1 + 3 + 9 = 13
Show Solution >
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FAQs on Factors of 9
What are the Factors of 9?
The factors of 9 are 1, 3, 9 and its negative factors are -1, -3, -9.
What is the Greatest Common Factor of 9 and 7?
The factors of 9 are 1, 3, 9 and the factors of 7 are 1, 7. 9 and 7 have only one common factor which is 1. This implies that 9 and 7 are co-prime.
Hence, the Greatest Common Factor (GCF) of 9 and 7 is 1.
What is the Sum of the Factors of 9?
All the Factors of 9 are 1, 3, 9 and therefore the sum of all these factors is 1 + 3 + 9 = 13
What are the Prime Factors of 9?
The prime factor of 9 is 3.
How Many Factors of 9 are also common to the Factors of 3?
Since, the factors of 9 are 1, 3, 9 and the factors of 3 are 1, 3.
Hence, [1, 3] are the common factors of 9 and 3.
