What is Meant by Factors?
A factor of a number is an integer that divides the number evenly, that is, with no remainder. In other words, we can say that if a number is divided by its factor, the remainder is zero. The quotient obtained in this division operation is also a factor of the number.
What are the Factors of 11?
The factors of 11 are those integers that divide 11 without leaving any remainder. In other words, we can say that the factors of 11 will divide 11 exactly. Additionally, factors cannot be decimals or fractions. The quotient obtained on dividing 11 by its factor is also a factor of 11.
The factors of 11
Factors | Factor pair | Prime factorization |
|---|---|---|
1, 11 | (1, 11) | 1 x 11 = 11 |
For example, 11 is a factor of 11 because when 11 is divided by 11, it leaves 0 as the remainder and 1 as the quotient. 1 is also a factor of 11.
Factor List for 11
Divisor | Is the number a factor of 11? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 11 = 11 |
2 | No, 11 is odd. | - |
3 | No, 1 + 1 = 2 is not divisible by 3 | - |
4 | No, 11 ÷ 4 = 2R3 | - |
5 | No, the ones digit is not 0 or 5. | - |
6 | No, 11 is odd and not divisible by 3. | - |
7 | No, 11 ÷ 7 = 1 R4 | - |
8 | No, 11 ÷ 8 = 1 R3 | - |
9 | No, 11 ÷ 9 = 1 R2 | - |
10 | No, one's digit is not 0 | - |
11 | Yes, 11 ÷ 11 = 1 R0 | 11 x 1 = 11 |
Hence, we can stop checking the factor pairs after 11 as the multiplication equation will start to repeat.
Hence, the factors of 11 are 1 and 11. Therefore, 11 is a prime number as it has only 2 factors: 1 and itself.
Prime Factorization of 11
A factor tree can be used to determine the prime factors of 11, as shown in the figure below.
From the factor tree, we can see that the prime factorization of 11 is 1 x 11.
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The Factor Pairs of 11
The factor pair of 11 is the set of two factors of 11 that when multiplied, give 11 as the product.
As 11 is prime, the only factor pair of 11 is:
Solved Factors of 11 Examples
Example 1: A school library has a collection of 11 books on the evolution of birds. The books are to be arranged evenly on 3 shelves, labeled ‘Biology’. The remaining books are kept with the librarian. How many books are with the librarian?
Solution:
Number of books = 11
Number of shelves = 3
Number of books on each shelf = \(\frac{11}{3}\) = 3 R2
So 3 books are placed on each shelf.
Total number of books placed on the shelf = Number of books on each shelf x Number of shelves
= 3 x 3
= 9
Number of books remaining = 11 -9 = 2
Therefore, the librarian has 2 books.
Example 2: Find the common factors of 17 and 11.
Solution:
Factors of 17: 1, 17
Factors of 11: 1, 11
So, the common factor of 11 and 17 is 1.
Hence, 17 and 11 have only one common factor.
Example 3: What are the common factors of 11 and 16?
Solution:
The factors of 11 are 1, 11
The factors of 16 are 1, 2, 4, 8,16
So, the common factor of 11 and 16 is 1.
Yes, 1 is a factor of 11. This is because the number 1 divides 11 exactly, that is, it leaves 0 as the remainder. So, 1 is a factor of 11.
No, 11 is not a composite number as it has only two factors. The factors of 11 are 1 and 11. Therefore, 11 is a prime number.
The factors of 11 are 1 and 11. So, the smallest factor of 11 is 1 and the greatest factor of 11 is 11 itself.
The factors of 11 are 1 and 11. Hence, the sum of the factors of 11 is = 1 + 11 = 12. Hence, the sum of the factors of 11, is 12.
The factors of 11 are 1 and 11. So, 11 has two factors.