# Factors of 990

Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990

#### How to find factors of a number

 1.   Find factors of 990 using Division Method 2.   Find factors of 990 using Prime Factorization 3.   Find factors of 990 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 990

• Divide 990 by 1: 990 ÷ 1 : Remainder = 0
• Divide 990 by 2: 990 ÷ 2 : Remainder = 0
• Divide 990 by 3: 990 ÷ 3 : Remainder = 0
• Divide 990 by 5: 990 ÷ 5 : Remainder = 0
• Divide 990 by 6: 990 ÷ 6 : Remainder = 0
• Divide 990 by 9: 990 ÷ 9 : Remainder = 0
• Divide 990 by 10: 990 ÷ 10 : Remainder = 0
• Divide 990 by 11: 990 ÷ 11 : Remainder = 0
• Divide 990 by 15: 990 ÷ 15 : Remainder = 0
• Divide 990 by 18: 990 ÷ 18 : Remainder = 0
• Divide 990 by 22: 990 ÷ 22 : Remainder = 0
• Divide 990 by 30: 990 ÷ 30 : Remainder = 0
• Divide 990 by 33: 990 ÷ 33 : Remainder = 0
• Divide 990 by 45: 990 ÷ 45 : Remainder = 0
• Divide 990 by 55: 990 ÷ 55 : Remainder = 0
• Divide 990 by 66: 990 ÷ 66 : Remainder = 0
• Divide 990 by 90: 990 ÷ 90 : Remainder = 0
• Divide 990 by 99: 990 ÷ 99 : Remainder = 0
• Divide 990 by 110: 990 ÷ 110 : Remainder = 0
• Divide 990 by 165: 990 ÷ 165 : Remainder = 0
• Divide 990 by 198: 990 ÷ 198 : Remainder = 0
• Divide 990 by 330: 990 ÷ 330 : Remainder = 0
• Divide 990 by 495: 990 ÷ 495 : Remainder = 0
• Divide 990 by 990: 990 ÷ 990 : Remainder = 0

Hence, Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990

#### 2. Steps to find factors of 990 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 990 using the division method, follow these steps:

• Step 1. Start dividing 990 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 990, which is 2. Divide 990 by 2 to obtain the quotient (495).
990 ÷ 2 = 495
• Step 3. Repeat step 1 with the obtained quotient (495).
495 ÷ 3 = 165
165 ÷ 3 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1

So, the prime factorization of 990 is, 990 = 2 x 3 x 3 x 5 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 990 as shown below:

So, the prime factorization of 990 is, 990 = 2 x 3 x 3 x 5 x 11.

#### 3. Find factors of 990 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 990 would be the two numbers which, when multiplied, give 990 as the result.

The following table represents the calculation of factors of 990 in pairs:

Factor Pair Pair Factorization
1 and 990 1 x 990 = 990
2 and 495 2 x 495 = 990
3 and 330 3 x 330 = 990
5 and 198 5 x 198 = 990
6 and 165 6 x 165 = 990
9 and 110 9 x 110 = 990
10 and 99 10 x 99 = 990
11 and 90 11 x 90 = 990
15 and 66 15 x 66 = 990
18 and 55 18 x 55 = 990
22 and 45 22 x 45 = 990
30 and 33 30 x 33 = 990

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 990. They are called negative pair factors.

Hence, the negative pairs of 990 would be ( -1 , -990 ) , ( -2 , -495 ) , ( -3 , -330 ) , ( -5 , -198 ) , ( -6 , -165 ) , ( -9 , -110 ) , ( -10 , -99 ) , ( -11 , -90 ) , ( -15 , -66 ) , ( -18 , -55 ) , ( -22 , -45 ) and ( -30 , -33 ) .

#### What are factors?

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

#### Properties of factors

• Each number is a factor of itself. Eg. 990 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990 are exact divisors of 990.
• 1 is a factor of every number. Eg. 1 is a factor of 990.
• Every number is a factor of zero (0), since 990 x 0 = 0.

• Which is the smallest prime factor of 990?

Smallest prime factor of 990 is 2.

• Is 990 a perfect square?

No 990 is not a perfect square.

• What are five multiples of 990?

First five multiples of 990 are 1980, 2970, 3960, 4950, 5940.

• What is prime factorization of 990?

Prime factorization of 990 is 2 x 3 x 3 x 5 x 11.

• What are factors of 990?

Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.

• How do you find factors of a negative number? ( eg. -990 )?

Factors of -990 are -1, -2, -3, -5, -6, -9, -10, -11, -15, -18, -22, -30, -33, -45, -55, -66, -90, -99, -110, -165, -198, -330, -495, -990.

• Is 990 a whole number?

Yes 990 is a whole number.

• Which is greatest factor of 990?

The greatest factor of 990 is 495.

• What are the prime factors of 990?

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
Prime factors of 990 are 2, 3, 3, 5, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 990. Can you help her?

Prime factors of 990 are 2, 3, 3, 5, 11.
Hence, the product of prime factors of 330.

Can you help Rubel to find out the product of the even factors of 990?

Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
Even factors of 990 are 2, 6, 10, 18, 22, 30, 66, 90, 110, 198, 330, 990.
Hence, product of even factors of 990 is; 2 x 6 x 10 x 18 x 22 x 30 x 66 x 90 x 110 x 198 x 330 x 990 = 60254729561664000000.

Joy wants to calculate mean of all the factors of 990. Help him in finding the mean of 990.

Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 990 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 11 + 15 + 18 + 22 + 30 + 33 + 45 + 55 + 66 + 90 + 99 + 110 + 165 + 198 + 330 + 495 + 990 = 2808.
Hence, the mean of factors of 990 is 2808 ÷ 24 = 117.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 990? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -11, -15, -18, -22, -30, -33, -45, -55, -66, -90, -99, -110, -165, -198, -330, -495, -990.

How many factors are there for 990?

Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
So there are in total 24 factors.

Joey wants to write all the prime factors of 990 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 990 are 2, 3, 3, 5, 11.
So in exponential form it can be written as 2 x 32 x 5 x 11.

Kevin has been asked to write 23 factor(s) of 990. Can you predict the answer?

23 factor(s) of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495.