123 LearnersLast updated on June 2nd, 2025
Factors of 1221
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1221, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1221?
The numbers that divide 1221 evenly are known as factors of 1221.
A factor of 1221 is a number that divides the number without remainder.
The factors of 1221 are 1, 3, 11, 33, 37, 111, 407, and 1221.
Negative factors of 1221: -1, -3, -11, -33, -37, -111, -407, and -1221.
Prime factors of 1221: 3, 11, and 37.
Prime factorization of 1221: 3 × 11 × 37.
The sum of the factors of 1221: 1 + 3 + 11 + 33 + 37 + 111 + 407 + 1221 = 1824
How to Find Factors of 1221?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1221.
Identifying the numbers which are multiplied to get the number 1221 is the multiplication method.
Step 1: Multiply 1221 by 1, 1221 × 1 = 1221.
Step 2: Check for other numbers that give 1221 after multiplying
3 × 407 = 1221
11 × 111 = 1221
33 × 37 = 1221
Therefore, the positive factor pairs of 1221 are: (1, 1221), (3, 407), (11, 111), (33, 37).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1221 by 1, 1221 ÷ 1 = 1221.
Step 2: Continue dividing 1221 by the numbers until the remainder becomes 0.
1221 ÷ 1 = 1221
1221 ÷ 3 = 407
1221 ÷ 11 = 111
1221 ÷ 33 = 37
Therefore, the factors of 1221 are: 1, 3, 11, 33, 37, 111, 407, 1221.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 1221 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1221 ÷ 3 = 407
407 ÷ 11 = 37
37 ÷ 37 = 1
The prime factors of 1221 are 3, 11, and 37.
The prime factorization of 1221 is: 3 × 11 × 37.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1221 is divided by 3 to get 407.
Step 2: Now divide 407 by 11 to get 37.
Step 3: 37 is a prime number and cannot be divided further. So, the prime factorization of 1221 is: 3 × 11 × 37.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1221: (1, 1221), (3, 407), (11, 111), and (33, 37).
Negative factor pairs of 1221: (-1, -1221), (-3, -407), (-11, -111), and (-33, -37).
Common Mistakes and How to Avoid Them in Factors of 1221
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1221, 1 and 1221 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1221 consist of -1, -3, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1221/1.5 = 814, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1221 are prime numbers. 3, 11, and 37 are the prime factors of 1221, but it has other factors like 33 and 407.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1221 as 3 × 11 × 37 and missing all the key factors.
Factors of 1221 Examples
Problem 1
There are 11 friends and 1221 candies. How will they divide it equally?
They will get 111 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1221/11 = 111
Problem 2
A rectangular garden has a length of 37 meters and a total area of 1221 square meters. What is the width?
33 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1221 = 37 × width
To find the value of the width, we need to shift 37 to the left side.
1221/37 = width
Width = 33.
Problem 3
There are 3 teams and 1221 tickets. How many tickets will each team get?
Each team will get 407 tickets.
Explanation
To find the number of tickets each team will get, divide the total tickets by the number of teams.
1221/3 = 407
Problem 4
A library has 1221 books and 407 shelves. How many books will be placed on each shelf?
There will be 3 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
1221/407 = 3
Problem 5
1221 chairs need to be arranged in 11 rows. How many chairs will be in each row?
Each row will have 111 chairs.
Explanation
Divide the total chairs by the number of rows.
1221/11 = 111
FAQs on Factors of 1221
1.What are the factors of 1221?
2.Mention the prime factors of 1221.
3.Is 1221 a multiple of 33?
4.Mention the factor pairs of 1221?
5.What is the square of 1221?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1221?
7.What are some fun ways kids in Qatar can practice Factors of 1221 with numbers?
8.What role do numbers and Factors of 1221 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1221 skills?
Important Glossaries for Factors of 1221
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1221 are 1, 3, 11, 33, 37, 111, 407, and 1221.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 37 are prime factors of 1221.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1221 are (1, 1221), (3, 407), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1221 is 3 × 11 × 37.
- Multiple: A number that can be divided by another number without a remainder. For example, 1221 is a multiple of 33.
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About BrightChamps in Qatar
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
