Factors of 9

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

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.

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:

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.

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.