Factors of 99—with division and prime factorization

Factors of 99

Factors of 99

Factors of 99 are the natural numbers that divide an original number completely. 

Therefore, if any factor divides 99, there is no remainder, and a quotient is a whole number. Take the number 8, whose factors are 1, 2, 4, and 8. As a result, dividing 8 by 4 gives us 2.

8 ÷ 4 = 2

As a result, there is no remainder, and a quotient is a whole number.

Similarly, we can find here in this article the factors of 99 as well as pair factors and prime factors. When multiplied together, pair factors result in the original number, and prime factors are the prime numbers that divide the original number evenly.

Factors of 99

What are Factors of -99?

When we multiply two numbers, and we get -99 as a product, that numbers are the factors of -99.

 Here is the explanation:

-1 × 99 = -99

 1 × -99 = -99

-3 × 33 = -99

 3 × -33 = -99

-9 × 11 = -99

 9 × -11 = -99

We can get -99 by having (-1, 99), (-3, 33), and(-9, 11), as a pair of factors. Similarly, we can also get -99 by having (1, -99), (3, -33), and(9, -11), as a pair of factors.

How to Find Factors of 99?

The factor of 99 is a real number/integer that divides the original number evenly, without any remainder. It has more than two factors because 99 is a composite number. The smallest natural number is 1, so we’ll divide 99 by 1.

99 ÷ 1 = 99

99 ÷ 3 = 33

99 ÷ 9 = 11

99 ÷ 11 = 9

99 ÷ 33 = 3

99 ÷ 99 = 1

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

Remember: 99 is an odd number, so it cannot be divided by an even number.

What are the Factors of 99?

To get a complete set of the factors of 99, we will learn the pair factors of 99.

Pair Factors of 99

If you multiply pair factors of 99, you will get the original number, which is as follows:

1 × 99 = 99

3 × 33 = 99

9 × 11 = 99

Thus, the pair factors are (1, 99), (3, 33), and (9, 11).

In this case, the pair factors were positive. When we consider negative pairs of factors, we can multiply the two negative numbers to get the original number.

-1 × -99 = 99

-3 × -33 = 99

-9 × -11 = 99

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

Prime Factorization of 99

A prime factor of 99 is the prime number that divides this number evenly. Alternatively, we can say that 99 is divisible by its prime factors. To find the prime factors, we will use the prime factorization method.

Factors of 99 by prime factorization

Step 1:

 When we divide 99 by the smallest prime factor, which is 3, we get;

99/3 = 33

Step 2: 

Divide 33 again by the smallest prime factor, 3, to get;

33/33 = 11

Step 3

Since 11 is a prime factor, it can only be divided by 11.

11/11 = 1

Thus,

Prime factorization of 99 = 3 × 3 × 11 = 32 × 11

Solved Examples

Q.1: 99 friends have to go to a conference. There are 33 seats available on the bus. How many students can be seated in one seat?

Solution

Given,

Number of friends = 99

Number of seats in a bus = 33

Number of students sitting in a seat = 99/33 = 3

Q.2: What is the sum of all 99 factors?

Solution:

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

Sum = 1+3+9+11+33+99 = 156

Thus, 156 is the required sum.

Q.3: What is the common factor between 11 and 99?

Solution

Both numbers have factors, so let’s write them down.

11 → 1, 11 (Since 11 is a prime number)

99 → 1, 3, 9, 11, 33, and 99 (99 is a composite number)

Hence, we can see the common factors are 1 and 11.

FAQ`s

1. How many factors are there for number 99?

There are six factors of 99 in total. These are 1, 3, 9, 11, 33, and 99.

2. Is 99 a prime number?

There are more than two factors in the number 99, so it isn’t a prime number.

3. What are the multiples of 99?

These are the first 10 multiples of 99: 99, 198, 297, 396, 495, 594, 693, 792, 891 and 990.

4. What is 99 as a product of primes?

The prime factorization of 99 = 3 × 3 × 11 = 32 × 11

5. What is the GCF of 99 and 100?

Factors of 99 = 1, 3, 9, 11, 33, 99

Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100

As a result, 99 and 100 shares one greatest common factor (GCF).

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