# Factors of 9

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.

#### 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 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:

#### 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.