Last updated on June 2nd, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 11 friends and 1221 candies. How will they divide it equally?
They will get 111 candies each.
To divide the candies equally, we need to divide the total candies with the number of friends.
1221/11 = 111
A rectangular garden has a length of 37 meters and a total area of 1221 square meters. What is the width?
33 meters.
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.
There are 3 teams and 1221 tickets. How many tickets will each team get?
Each team will get 407 tickets.
To find the number of tickets each team will get, divide the total tickets by the number of teams.
1221/3 = 407
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.
Dividing the books by the total shelves, we will get the number of books on each shelf.
1221/407 = 3
1221 chairs need to be arranged in 11 rows. How many chairs will be in each row?
Each row will have 111 chairs.
Divide the total chairs by the number of rows.
1221/11 = 111
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.
: She loves to read number jokes and games.