Factors of 121
Factors of 121 are the list of integers that we can split evenly into 121. There are 3 factors of 121 of which 121 itself is the biggest factor and its positive factors are 1, 11 and 121. The Prime Factors of 121 are 1, 11, 121 and its Factors in Pairs are (1, 121) and (11, 11).
- Factors of 121: 1, 11 and 121
- Negative Factors of 121: -1, -11 and -121
- Prime Factors of 121: 11
- Prime Factorization of 121: 11 × 11 = 112
- Sum of Factors of 121: 133
| 1. | What are Factors of 121? |
| 2. | How to Calculate Factors of 121? |
| 3. | Factors of 121 by Prime Factorization |
| 4. | Factors of 121 in Pairs |
| 5. | FAQs on Factors of 121 |
What are Factors of 121?
The factor of a number is that number that divides it completely i.e. leaving no remainder. In order to find the factors of the number 121, we will have to perform division on 121 and find the numbers which divide 121 completely, leaving no remainders.
How to Calculate the Factors of 121?
There are two common methods to find the factors of 121.
- Division method
- Prime factorization method
Let us try to find using the division method:
- We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc up to 61( approximate half of 121) respectively.
- The number 1 and the number itself would always be a factor of the given number.
- Refer to the following table to check division 121 by its factors:
| Divide | Result |
|
121÷ 1 |
Gives remainder 0 So, 1 is a factor. |
| 121 ÷ 11 |
Gives remainder 0 So, 11 is a factor. |
| 121 ÷ 121 |
Gives remainder 0 So, 121 is a factor. |
Hence, the factors of 121 are 1, 11 , and 121. Explore factors using illustrations and interactive examples:
- Factors of 120: The factors of 120 are 1, 2 ,3, 4, 5, 6, 8,10,12,15, 20, 24, 30, 60 and 120
- Factors of 144: The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
- Factors of 169: The factors of 169 are 1, 13 and 169
- Factors of 33: The factors of 33 are 1,3,11, and 33.
- Factors of 81: The factors of 81 are 1, 3, 9, 27, and 81.
Tips and Tricks
- Use the divisibility rule of different prime factors to find the prime factorization of 121.
- The prime factorization of 121 is 11 × 11 or 112, then add 1 to the exponent. i.e. 2 + 1 = 3. We have 3 distinct factors of 121.
Factors of 121 by Prime Factorization
Prime factorization is expressing the number as the product of its prime factors.
- Step 1: Start dividing 121 from the smallest prime number i.e., 2, followed by 3, 5, and so on to find the smallest prime factor of the number.
- Step 2: After finding the smallest prime factor of the number 121 i.e., 11, divide 121 by 11 to obtain the quotient 11.
- Step 3: The obtained quotient is a prime number itself. The division procedure can thus be terminated at this step.
So, the Prime factorization of 121 is: 121 = 11 × 11 = 112
Factors of 121 in Pairs
- Positive pair factors of 121 : (1,11), (11,11), (1,121)
- Negative pair factors of 121 : (-1, -11), (-11, -11), (-1, -121)
Important Notes:
- Only whole numbers and integers can be converted to factors.
- Only composite numbers can have more than two factors.
- The smallest factor of a number is 1 and the biggest factor of a number would be the number itself.
FAQs on Factors of 121
What are the Factors of 121?
The factors of 121 are 1, 11, 121 and its negative factors are -1, -11, -121.
What is the Sum of the Factors of 121?
Since all factors of 121 are 1, 11, 121 therefore, the sum of its factors is 1 + 11 + 121 = 133.
What is the Greatest Common Factor of 121 and 53?
The factors of 121 are 1, 11, 121 and the factors of 53 are 1, 53. 121 and 53 have only one common factor which is 1. This implies that 121 and 53 are co-prime.
Hence, the Greatest Common Factor (GCF) of 121 and 53 is 1.
What are the Pair Factors of 121?
The pair factors of 121 are (1, 121), (11, 11).
How Many Factors of 66 are also common to the Factors of 121?
Since the factors of 121 are 1, 11, 121, and the factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Hence, [1, 11] are the common factors of 121 and 66.