Definition of factors of 9: If a number completely divides 9 without leaving a remainder, then that number is called a factor of 9.
By the above definition, we can say that the factors of 9 are the divisors of 9. In this section, we will learn about the factors of 9 and the prime factors of 9.
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Highlights of Factors of 9
- 9=3×3 is the prime factorization of 9.
- The factors of 9 are 1, 3, and 9.
- The only prime factor of 9 is 3.
- Negative factors of 9 are –1, -3, and –9.
What are the factors of 9?
Let us write the number 9 multiplicatively in all possible ways. We definitely have:
9 = 1×9
9 = 3×3
We cannot write 9 multiplicatively in any other way than the above ones, so we will stop right now. Thus the factors of 9 in pairs are given as follows:
| 9 = a×b | Factors in Pairs (a,b) |
| 9 = 1×9 | (1, 9) |
| 9 = 3×3 | (3, 3) |
Thus the pair factors of 9 are (1, 9) and (3, 3). As all the numbers appearing in pair factors are the factors of 9, we conclude that
|
The factors of 9 are: 1, 3, and 9. |
Number of factors of 9
From above we have calculated the factors of 9 which are 1, 3, and 9. Thus the total number of factors of 9 is three.
Prime Factors of 9
Note that the factors of 9 are 1, 3, and 9. Among those factors, we observe that only 3 is a prime number as 3 does not have any proper divisors.
∴ the only prime factor of 9 is 3.
Question: What are the factors of 9?
Video Solution:
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How to find factors of 9?
Now we will determine the factors of 9 by division method. In this method, we will try to find the numbers that can divide 9 with no remainder. See that
9/1=9 and the remainder is 0.
∴ 1 and 9 are factors of 9.
9/3=3 and the remainder is 0.
∴ 3 and 3 are factors of 9 ⇒ 3 is a factor of 9.
Note that no numbers other than the numbers in violet color can divide 9. So the numbers in violet color, that is, 1, 3, and 9 are the complete list of factors of 9.
