Factors of 99

The numbers that divide 99 evenly are known as factors of 99. A factor of 99 is a number that divides the number without remainder. The factors of 99 are 1, 3, 9, 11, 33, and 99.

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

Prime factors of 99: 3 and 11.

Prime factorization of 99: 3² × 11.

The sum of factors of 99: 1 + 3 + 9 + 11 + 33 + 99 = 156

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 99. Identifying the numbers which are multiplied to get the number 99 is the multiplication method.

Step 1: Multiply 99 by 1, 99 × 1 = 99.

Step 2: Check for other numbers that give 99 after multiplying 3 × 33 = 99

9 × 11 = 99

Therefore, the positive factor pairs of 99 are: (1, 99), (3, 33), (9, 11). All these factor pairs result in 99. For every positive factor, there is a negative factor.

Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 99 by 1, 99 ÷ 1 = 99.

Step 2: Continue dividing 99 by the numbers until the remainder becomes 0.

99 ÷ 1 = 99

99 ÷ 3 = 33

99 ÷ 9 = 11

Therefore, the factors of 99 are: 1, 3, 9, 11, 33, 99.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 99 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

99 ÷ 3 = 33

33 ÷ 3 = 11

11 ÷ 11 = 1

The prime factors of 99 are 3 and 11. The prime factorization of 99 is: 3² × 11.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 99 is divided by 3 to get 33.

Step 2: Now divide 33 by 3 to get 11.

Step 3: Here, 11 is a prime number, that cannot be divided anymore. So, the prime factorization of 99 is: 3² × 11.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 99: (1, 99), (3, 33), (9, 11).
• Negative factor pairs of 99: (-1, -99), (-3, -33), (-9, -11).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 99 are 1, 3, 9, 11, 33, and 99.

• Prime factors: The factors which are prime numbers. For example, 3 and 11 are prime factors of 99.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 99 are (1, 99), (3, 33), etc.

• Prime factorization: A method of expressing a number as the product of its prime factors. For example, the prime factorization of 99 is 3² × 11.

• Multiplication method: A way to find factors by identifying pairs of numbers that multiply to give the target number, like (9, 11) for 99.