Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 441, how they are used in real life, and tips to learn them quickly.
The numbers that divide 441 evenly are known as factors of 441.
A factor of 441 is a number that divides the number without a remainder.
The factors of 441 are 1, 3, 9, 21, 49, 63, 147, and 441.
Negative factors of 441: -1, -3, -9, -21, -49, -63, -147, and -441.
Prime factors of 441: 3 and 7.
Prime factorization of 441: 32 × 72.
The sum of factors of 441: 1 + 3 + 9 + 21 + 49 + 63 + 147 + 441 = 734
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 441. Identifying the numbers that are multiplied to get the number 441 is the multiplication method.
Step 1: Multiply 441 by 1, 441 × 1 = 441.
Step 2: Check for other numbers that give 441 after multiplying
3 × 147 = 441
9 × 49 = 441
21 × 21 = 441
Therefore, the positive factor pairs of 441 are: (1, 441), (3, 147), (9, 49), (21, 21). All these factor pairs result in 441.
For every positive factor, there is a negative factor.
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 441 by 1, 441 ÷ 1 = 441.
Step 2: Continue dividing 441 by the numbers until the remainder becomes 0.
441 ÷ 1 = 441
441 ÷ 3 = 147
441 ÷ 9 = 49
441 ÷ 21 = 21
Therefore, the factors of 441 are: 1, 3, 9, 21, 49, 63, 147, 441.
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 441 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 441 are 3 and 7.
The prime factorization of 441 is: 32 × 72 .
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 441 is divided by 3 to get 147.
Step 2: Now divide 147 by 3 to get 49.
Step 3: Then divide 49 by 7 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 441 is: 32 × 72 .
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 441: (1, 441), (3, 147), (9, 49), (21, 21).
Negative factor pairs of 441: (-1, -441), (-3, -147), (-9, -49), (-21, -21).
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 9 students and 441 candies. How will they divide it equally?
They will get 49 candies each.
To divide the candies equally, we need to divide the total candies by the number of students.
441/9 = 49
A garden is square-shaped, and the total area is 441 square meters. Find the length of one side?
21 meters.
To find the length of one side of the square, we use the formula,
Area = side × side
441 = side × side
The square root of 441 = side
Side = 21.
There are 21 boxes and 441 apples. How many apples will be in each box?
Each box will have 21 apples.
To find the apples in each box, divide the total apples by the boxes.
441/21 = 21
In a stadium, there are 63 rows, and 441 seats. How many seats are there in each row?
There are 7 seats in each row.
Dividing the seats by the total rows, we will get the number of seats in each row.
441/63 = 7
441 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 63 books.
Divide total books by shelves.
441/7 = 63
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.