# Factors of 110

Factors of 110 are 1, 2, 5, 10, 11, 22, 55, and 110

#### How to find factors of a number

 1.   Find factors of 110 using Division Method 2.   Find factors of 110 using Prime Factorization 3.   Find factors of 110 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 110

• Divide 110 by 1: 110 ÷ 1 : Remainder = 0
• Divide 110 by 2: 110 ÷ 2 : Remainder = 0
• Divide 110 by 5: 110 ÷ 5 : Remainder = 0
• Divide 110 by 10: 110 ÷ 10 : Remainder = 0
• Divide 110 by 11: 110 ÷ 11 : Remainder = 0
• Divide 110 by 22: 110 ÷ 22 : Remainder = 0
• Divide 110 by 55: 110 ÷ 55 : Remainder = 0
• Divide 110 by 110: 110 ÷ 110 : Remainder = 0

Hence, Factors of 110 are 1, 2, 5, 10, 11, 22, 55, and 110

#### 2. Steps to find factors of 110 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 110 using the division method, follow these steps:

• Step 1. Start dividing 110 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 110, which is 2. Divide 110 by 2 to obtain the quotient (55).
110 ÷ 2 = 55
• Step 3. Repeat step 1 with the obtained quotient (55).
55 ÷ 5 = 11
11 ÷ 11 = 1

So, the prime factorization of 110 is, 110 = 2 x 5 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 110 as shown below:

So, the prime factorization of 110 is, 110 = 2 x 5 x 11.

#### 3. Find factors of 110 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 110 would be the two numbers which, when multiplied, give 110 as the result.

The following table represents the calculation of factors of 110 in pairs:

Factor Pair Pair Factorization
1 and 110 1 x 110 = 110
2 and 55 2 x 55 = 110
5 and 22 5 x 22 = 110
10 and 11 10 x 11 = 110

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 110. They are called negative pair factors.

Hence, the negative pairs of 110 would be ( -1 , -110 ) , ( -2 , -55 ) , ( -5 , -22 ) and ( -10 , -11 ) .

#### 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. 110 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, 5, 10, 11, 22, 55, 110 are exact divisors of 110.
• 1 is a factor of every number. Eg. 1 is a factor of 110.
• Every number is a factor of zero (0), since 110 x 0 = 0.

• What two numbers make 110?

Two numbers that make 110 are 2 and 55.

• What is prime factorization of 110?

Prime factorization of 110 is 2 x 5 x 11.

• Write some multiples of 110?

First five multiples of 110 are 220, 330, 440, 550.

• Which is the smallest prime factor of 110?

The smallest prime factor of 110 is 2.

• Is 110 a perfect square?

No 110 is not a perfect square.

• What is the sum of all factors of 110?

The sum of all factors of 110 is 216.

• What are factors of 110?

Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.

• How do you find factors of a negative number? ( eg. -110 )?

Factors of -110 are -1, -2, -5, -10, -11, -22, -55, -110.

• Is 110 a whole number?

Yes 110 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 110. Help him in finding the mean of 110.

Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 110 is 1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 = 216.
Hence, the mean of factors of 110 is 216 ÷ 8 = 27.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 110? Help her in writing all the factors.

Positive factors are 1, 2, 5, 10, 11, 22, 55, 110.
Negative factors are -1, -2, -5, -10, -11, -22, -55, -110.

Joey wants to write all the prime factors of 110 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 110 are 2, 5, 11.
So in exponential form it can be written as 2 x 5 x 11.

Kevin has been asked to write 7 factor(s) of 110. Can you predict the answer?

7 factor(s) of 110 are 1, 2, 5, 10, 11, 22, 55.

Sammy is puzzled while calculating the prime factors of 110. Can you help him find them?

Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
Prime factors of 110 are 2, 5, 11

What is prime factorization of 110?

Prime factorization of 110 is 2 x 5 x 11 = 2 x 5 x 11.

Can you help Rubel to find out the product of the even factors of 110?

Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
Even factors of 110 are 2, 10, 22, 110.
Hence, product of even factors of 110 is; 2 x 10 x 22 x 110 = 48400.