Factors of 9

2. Steps to find factors of 9 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 9 using the division method, follow these steps:

• Step 1. Start dividing 9 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 9, which is 3. Divide 9 by 3 to obtain the quotient (3).
  9 ÷ 3 = 3
• Step 3. Repeat step 1 with the obtained quotient (3).
  3 ÷ 3 = 1

So, the prime factorization of 9 is, 9 = 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 9 as shown below:

So, the prime factorization of 9 is, 9 = 3 x 3.

3. Find factors of 9 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 9 would be the two numbers which, when multiplied, give 9 as the result.

The following table represents the calculation of factors of 9 in pairs:

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 9. They are called negative pair factors.

Hence, the negative pairs of 9 would be ( -1 , -9 ) , ( -3 , -3 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 9 are exact divisors of 9.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 9 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 9.

Frequently Asked Questions

• Which is the smallest prime factor of 9?

  Smallest prime factor of 9 is 3.

• Is 9 a perfect square?

  Yes 9 is a perfect square.

• What are five multiples of 9?

  First five multiples of 9 are 18, 27, 36, 45, 54.

• What is prime factorization of 9?

  Prime factorization of 9 is 3 x 3.

• What are factors of 9?

  Factors of 9 are 1, 3, 9.

• How do you find factors of a negative number? ( eg. -9 )?

  Factors of -9 are -1, -3, -9.

• Is 9 a whole number?

  Yes 9 is a whole number.

• Which is greatest factor of 9?

  The greatest factor of 9 is 3.

• What are the prime factors of 9?

  The factors of 9 are 1, 3, 9.
  Prime factors of 9 are 3, 3.

Examples of Factors