Factors of 99 | Prime Factorization of 99 | Factor Tree of 99

The factors of a number are the numbers that divide the given number completely and evenly. The factors of a number can be both positive and negative. In this article, you will learn about the factors of 99 using the division method, prime factorization method, and factor tree method.

What Are the Factors of 99?

The factors of the number 99 are the numbers that can divide the number 99 thoroughly and evenly without leaving behind any remainders. The factors of a number can be both positive and negative. Apart from this, the factors of a number can be classified as prime numbers and composite numbers. Prime numbers are the numbers that have two or less than two numbers as the factors and composite numbers are the numbers that have more than two numbers as its factors. Here, the number 99 is a composite number as it has more than two numbers as its factors. The factors of 99 are 1, 3, 9, 11, 33, and 99.

Factors of 99: 1, 3, 9, 11, 33, and 99.

Negative Factors of 99: -1, -3, -9, -11, -33, and -99.

Prime Factorization of 99: 1 x 3

Pair Factors of 99: (1, 99), (3, 33), and (9, 11).

Prime Factors of 99: 3 and 11

Sum of Factors of 99: 156

Sum of Prime Factors of 99: 14

What Are the Factors of 99 in Pairs?

A number can have both positive and negative factors. A pair factor of a number is a combination of two numbers and on multiplying both numbers, the resultant should always be the given number. In this case, it has to be 99.

Positive Pair Factors of 99

The positive pair factors of 99 are (1, 99), (3, 33), and (9, 11).

Negative Pair Factors of 99

The negative pair factors of 99 are (-1, -99), (-3, -33), and (-9, -11).

How to Find Factors of 99 Through Division Method?

The factors of 99 can be determined using the long division method. In this method, the number 99 is divided by a sequence of natural integers. The numbers that divide the number 99 without leaving behind any remainder are known as the factors of 99. The following are the steps through which we can identify the factors of the number 99.

• 99 ÷ 1 = 99
• 99 ÷ 3 = 33
• 99 ÷ 9 = 11
• 99 ÷ 11 = 9
• 99 ÷ 33 = 3
• 99 ÷ 99 = 1
  

Therefore, the numbers 1, 3, 9, 11, 33, and 99 can divide the number 99 completely and evenly without having any decimal points. Hence, the factors of the number 99 are 1, 3. 11, 33, and 99.

What Is the Prime Factorization of 99?

Through the method of prime factorization, we can identify the prime factors of 99. In order to apply the prime factorization method to a number, it’s very important to know whether the given number is a prime number or a composite number. Here, 99 is a composite number as it has more than two factors and so the prime factors can be found by using this method. The following are the steps involved in it:

• Step 1: Let’s place the number 99 at the top, and divide it by the smallest number that can divide the given number 99 without any decimals and it is 3.
  99.
  99 ÷ 3 = 11
• Step 2: We get 33, as the quotient, and again it’s divisible by the number 3.
  33 ÷ 3 = 11
• Step 3: Now the quotient is 11, as it’s a prime number 11 is divisible by itself.
  11 ÷ 11 = 1
• Step 4: And in the final step, we get 1 as the quotient and it cannot be divided further. So the prime factors of 99 are 3, and 11.

Therefore, the prime factors of 99 are 3 and 11. Its well represented through the image given below:

What Is the Factor Tree of 99?

A factor tree is another method that is used to identify the prime factors of 99. In this method, let’s place the number 99 at the top of the factor tree. Now, split the pair factors of the number into two branches and this process should be continued until the branches become prime factors. Now circle the prime factors of 99.

• Step 1: Let’s place the number 99 at the top of the factor tree and write down the pair factors 3, and 33 in two branches.
• Step 2: Now let’s put the pair factors of 33 in the branches, which are 3 and 11.
• Step 3: And now the numbers 3 and 11 are prime numbers, we can’t further divide them as they are divisible by themselves.
• Step 4: So, now let’s circle the numbers 3 and 11.

Therefore, the prime factors of 99 are 3 x 11. Below is an image representation of the factor tree of 99.

Solved Examples of 99

What are the factors of 99?
The factors of 99 are 1, 3, 9, 11, 33, and 99.

What are the negative factors of 99?
The negative factors of 99 are -1, -3, -9, -11, -33, and -99.

What is the sum of the prime factors of 99?
The sum of the prime factors of 99 is 14.

What are the pair factors of 99?
The pair factors of 99 are (1, 99), (3, 33), and (9, 11).

Frequently Asked Questions

What is the prime factorization of 99?
Through the method of prime factorization, we can identify the prime factors of 99. In order to apply the prime factorization method to a number, it’s very important to know whether the given number is a prime number or a composite number. Here, 99 is a composite number as it has more than two factors and so the prime factors can be found by using this method. The following are the steps involved in it:
Step 1: Let’s place the number 99 at the top of the factor tree and write down the pair factors 3, and 33 in two branches.
Step 2: Now let’s put the pair factors of 33 in the branches, which are 3 and 11.
Step 3: And now the numbers 3 and 11 are prime numbers, we can’t further divide them as they are divisible by themselves.
Step 4: So, now let’s circle the numbers 3 and 11.
Therefore, the prime factors of 99 are 3 x 11. Below is an image representation of the factor tree of 99.

What are multiples of 99?
The first ten multiples of 99 are 99, 198, 297, 396, 495, 594, 693, 792, 891, and 990.

What is the root of 99?
The square root of 99 is 99 is 3√11 or 9.94.

Is 99 a multiple of 4?
No, 99 is not a multiple of 4, as 99 is not completely and evenly divisible by 4.

Can 9 be a multiple of 9?
Yes, 9 can be a multiple of 9. As 9 x 1 = 9.