# Factors of 11

Factors of 11 are 1 and 11

#### How to find factors of a number

 1.   Find factors of 11 using Division Method 2.   Find factors of 11 using Prime Factorization 3.   Find factors of 11 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 11

• Divide 11 by 1: 11 ÷ 1 : Remainder = 0
• Divide 11 by 11: 11 ÷ 11 : Remainder = 0

Hence, Factors of 11 are 1 and 11

#### 2. Steps to find factors of 11 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 11 using the division method, follow these steps:

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

So, the prime factorization of 11 is, 11 = 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 11 as shown below:

So, the prime factorization of 11 is, 11 = 11.

#### 3. Find factors of 11 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 11 would be the two numbers which, when multiplied, give 11 as the result.

The following table represents the calculation of factors of 11 in pairs:

Factor Pair Pair Factorization
1 and 11 1 x 11 = 11

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 11. They are called negative pair factors.

Hence, the negative pairs of 11 would be ( -1 , -11 ) , .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 11 x 0 = 0.
• 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, 11 are exact divisors of 11.
• Factors of 11 are 1, 11. Each factor divides 11 without leaving a remainder.

• What two numbers make 11?

Two numbers that make 11 are 11 and 1.

• What is prime factorization of 11?

Prime factorization of 11 is 11.

• Write some multiples of 11?

First five multiples of 11 are 22, 33, 44, 55.

• Which is the smallest prime factor of 11?

The smallest prime factor of 11 is 11.

• Is 11 a perfect square?

No 11 is not a perfect square.

• What is the sum of all factors of 11?

The sum of all factors of 11 is 12.

• What are factors of 11?

Factors of 11 are 1, 11.

• How do you find factors of a negative number? ( eg. -11 )?

Factors of -11 are -1, -11.

• Is 11 a whole number?

Yes 11 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 11. Help him in finding the mean of 11.

Factors of 11 are 1, 11.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 11 is 1 + 11 = 12.
Hence, the mean of factors of 11 is 12 ÷ 2 = 6.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 11? Help her in writing all the factors.

Positive factors are 1, 11.
Negative factors are -1, -11.

Joey wants to write all the prime factors of 11 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 11 are 11.
So in exponential form it can be written as 11.

Kevin has been asked to write 1 factor(s) of 11. Can you predict the answer?

1 factor(s) of 11 is 1.

Sammy is puzzled while calculating the prime factors of 11. Can you help him find them?

Factors of 11 are 1, 11.
Prime factors of 11 are 11

What is prime factorization of 11?

Prime factorization of 11 is 11 = 11.

Can you help Rubel to find out the product of the even factors of 11?

Factors of 11 are 1, 11.
Even factors of 11 are 0.
Hence, product of even factors of 11 is; 0 = 0.