The factor of 11

Factors of 11 are integers that can be divided evenly into 11. There are a total of 2 factors of 11 i.e. 1 and 11. The sum of all factors of 11 is 12 and its factors in Pairs are (1, 11).

• Factors of 11: 1 and 11
• Negative Factors of 11: -1 and -11
• Prime Factors of 11: 11
• Prime Factorization of 11: 11
• Sum of Factors of 11: 12

What Are the Factors of 11?

The factors of 11 are 1 and 11.  As 1 ×11 is 11 and 11 × 1 is also 11.
The number 11 is a prime number.
A prime number has only two factors, 1 and the number itself.

Think Tank:

• Can 11 have zero as its factor?
• Can the factors of 11 be its multiples too?

How to Calculate the Factors of 11?

No matter what the number is, to find out the factors of any number, we try to divide the given number (11 in this case) by the smallest prime number and move up the order. It is continued till we reach the number, and identify the numbers that leave the remainder as 0 after division. Or, we try to make all the possible pairs of numbers that can give the product 11. The only possible pair of numbers which can give a product 11 is 1 and 11. The only factors of 11 are 1 and 11.

Hence, the factors of 11 are 1 and 11.

Explore factors using illustrations and interactive examples.

• Factors of 121 - The factors of 121 are 1, 11, 121
• Factors of 110 - The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110
• Factors of 112 - The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
• Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39, 117
• Factors of 119 - The factors of 119 are 1, 7, 17, 119
• Factors of 23 - The factors of 23 are 1, 23

Factors of 11 by Prime Factorization

Prime factorization is the process of expressing a number as a product of prime numbers. No number other than 1 and 11 divides 11 exactly, so by prime factorization, factors of 11 are 1 and 11.
Since only 1 and 11 are the factors of 11, 11 is a prime number.

Important Notes:

• To find the factors of any number, we can apply the divisibility rule.
• A number cannot have a decimal and a fraction as its factor. It can only have a positive integer as its factor.
• 11 has only two factors, 1 and 11.
• 11 is an odd prime number.

Factors of 11 in Pairs

Pair factor is the pair of any two numbers which, when multiplied, give a particular number.
Hence, pair factors of 11 are:

Pair factors can be negative too as the product of two negative numbers also results in a positive number. 
Hence, the pair factors of 11 are, (1, 11), (11, 1), (-1, -11), and (-11, -1) where (-1, -11) and (-11, -1) are the negative pair factors.

Factors of 11 Solved Examples

1. Example 1: Mary went to an orphanage to distribute the 22 cupcakes that she bought for the kids. There were 11 kids in the orphanage. Mary wants to distribute all the cupcakes equally to the kids. How many cupcakes will each child get?

   Solution:

   From the question, we know that Mary has 22 cupcakes and there are 11 kids in the orphanage.
   Now, we know that 22 is one of the multiples of 11; we can divide 22 by 11.

   On successful division, we get the answer as 2.
   Hence, the kids will get 2 cupcakes each.

2. Example 2: Sarah has 10 friends. She purchased a total of 55 notebooks for her friends and herself, if she wants to distribute these notebooks equally among her friends and also wants to keep an equal number of boxes for herself, how many notebooks will each of them get?

   Solution:

   From the question, we know that Sarah has 10 friends and the total number of notebooks is 55.
   Now, as Sarah also wants to keep an equal number of notebooks with herself, so the total number of people will be 11, not 10.

   Therefore, we have to divide 55 notebooks among 11 kids. Since we know that 55 is one of the multiples of 11, we will easily get the answer, which is 55/11 = 5.
   Hence, every kid will get 5 notebooks.

3. Example 3: Can you help Diana get the number which on multiplication to (-11) gives 11?       

   Solution:

   The negative factor pair of 11 is (-1, -11). 
   So when we multiply -11 by -1, we will get:

     -1 × -11 = 11

   Hence, she will have to multiply it by -1. 

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FAQs on Factors of 11

What are the Factors of 11?

The factors of 11 are 1, 11 and its negative factors are -1, -11.

What numbers are the Pair Factors of 11?

The pair factors of 11 are (1, 11).

What is the Greatest Common Factor of 11 and 4?

The factors of 11 are 1, 11 and the factors of 4 are 1, 2, 4. 11 and 4 have only one common factor which is 1. This implies that 11 and 4 are co-prime.

Hence, the Greatest Common Factor (GCF) of 11 and 4 is 1.

What is the Sum of the Factors of 11?

All the Factors of 11 are 1, 11 and therefore the sum of all these factors is 1 + 11 = 12

How Many Factors of 11 are also common to the Factors of 3?

Since the factors of 11 are 1, 11 and factors of 3 are 1, 3. Hence, 11 and 3 have only one common factor which is 1. Therefore, 11 and 3 are co-prime.

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