Factors of 121 Using Prime Factorization
- What are the Factors of 121?
- List of the Factors of 121
- The Prime Factorization of 121
- Factor Pairs of 121
- Solved Examples
- Frequently Asked Questions
What are the Factors of 121?
If the number 121 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 121. Here, the quotient obtained on division is also a factor of 121.
The factors of 121 are 1, 11, and 121 because all these numbers divide the number 121 evenly.
List of the Factors of 121
Divisibility rules and division facts applied to determine the factors of 121.
Divisor | Is the number a factor of 121? | Multiplication equation |
1 | Yes, 1 is a factor of every number. | 1 x 121 = 121 |
2 | No, 121 is not even. | – |
3 | No, 1 + 2 + 1 = 4 is not divisible by 3. | – |
4 | No, as 121 ÷ 4 = 30, and the remainder = 1 | – |
5 | No,ones digit is neither 0 nor 5. | – |
6 | No, 121 is not even. | – |
7 | No, as 121 ÷ 7 = 17 and the remainder = 2 | – |
8 | No, as 121 ÷ 8 = 15 and the remainder = 1 | – |
9 | No, as 121 ÷ 9 = 13 and the remainder = 4 | – |
10 | No, ones digit is not 0. | – |
11 | Yes, 121 ÷ 11 = 11 | 11 x 11 = 121 |
We can stop checking the factor pairs after 11 as they begin to repeat.
So, the factors of 121 are 1, 11, and 121.
[Note: If we divide 121 by 12, we get the quotient and remainder as 10 and 1, respectively. So, 12 is not a factor of 121. Similarly, you can check for other numbers as well.]
The Prime Factorization of 121
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 121 can be represented by using a factor tree as shown below.
So, the prime factorization of 121 is 121 = 11 x 11 or 11\(^2\), and the prime factor of 121 is 11.
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Factor Pairs of 121
A factor pair of a number is a set of any of its two factors such that their product is the number itself. A factor pair can be negative or positive.
The positive factor pairs of 121 are (1, 121) and (11, 11).
1 x 121 = 121
11 x 11 = 121
Positive factor pairs of 121
Positive Factors of 121 | Positive Factor Pairs of 121 |
1 x 121 | (1, 121) |
11 x 11 | (11, 11) |
Solved Factors of 121 Examples
Example 1: Find the common factors of 120 and 121.
Solution:
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
Factors of 121 = 1, 11, and 121
Therefore, the common factor of 120 and 121 is 1.
Example 2: Find the greatest common factor of 88 and 121.
Solution:
Factors of 88 = 1, 2, 4, 8, 11, 22, 44, and 88
Factors of 121 = 1, 11, and 121.
So, the common factors of 88 and 121 are 1 and 11.
Therefore, the greatest common factor of 88 and 121 is 11.
Example 3: John was studying geometrical shapes and found a rectangle of area 121 square centimeters. What are the possible dimensions of this rectangle?
Solution:
The area of the rectangle is 121 cm\(^2\).
Area of rectangle = length x width
121 = length x width
So, the dimensions of the rectangle will be the factor pairs of 121, which are, (1, 121), (11, 11), and (121, 1)
Therefore, the possible dimensions of the rectangle are:
Length in centimeters | Breadth in centimeters |
1 | 121 |
11 | 11 |
121 | 1 |
Frequently Asked Questions on Factors of 121
The factors of 121 are the numbers that divide 121 exactly, leaving the remainder as zero. The number 121 is exactly divisible by 1, 11, and 121 only. So, the factors of 121 are 1, 11, and 121.
Composite numbers are those numbers which have a factor other than 1 and itself, that is, a composite number has more than two factors.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.
Yes, because we get 121 by multiplying 11 into 11. So, we can say that 121 is a square of 11.
