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 462, how they are used in real life, and tips to learn them quickly.
The numbers that divide 462 evenly are known as factors of 462.
A factor of 462 is a number that divides the number without a remainder.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, and 462.
Negative factors of 462: -1, -2, -3, -6, -7, -11, -14, -21, -22, -33, -42, -66, -77, -154, -231, and -462.
Prime factors of 462: 2, 3, 7, and 11.
Prime factorization of 462: 2 × 3 × 7 × 11.
The sum of factors of 462: 1 + 2 + 3 + 6 + 7 + 11 + 14 + 21 + 22 + 33 + 42 + 66 + 77 + 154 + 231 + 462 = 1160
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 462. Identifying the numbers which are multiplied to get the number 462 is the multiplication method.
Step 1: Multiply 462 by 1, 462 × 1 = 462.
Step 2: Check for other numbers that give 462 after multiplying:
2 × 231 = 462
3 × 154 = 462
6 × 77 = 462
7 × 66 = 462
11 × 42 = 462
14 × 33 = 462
21 × 22 = 462
Therefore, the positive factor pairs of 462 are: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).
For every positive factor, there is a negative factor.
Dividing the given numbers with the 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 the simple division method:
Step 1: Divide 462 by 1, 462 ÷ 1 = 462.
Step 2: Continue dividing 462 by the numbers until the remainder becomes 0.
462 ÷ 1 = 462
462 ÷ 2 = 231
462 ÷ 3 = 154
462 ÷ 6 = 77
462 ÷ 7 = 66
462 ÷ 11 = 42
462 ÷ 14 = 33
462 ÷ 21 = 22
Therefore, the factors of 462 are: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.
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 462 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
462 ÷ 2 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 462 are 2, 3, 7, and 11.
The prime factorization of 462 is: 2 × 3 × 7 × 11.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 462 is divided by 2 to get 231.
Step 2: Now divide 231 by 3 to get 77.
Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 462 is: 2 × 3 × 7 × 11.
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 462: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).
Negative factor pairs of 462: (-1, -462), (-2, -231), (-3, -154), (-6, -77), (-7, -66), (-11, -42), (-14, -33), (-21, -22).
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 77 students and 462 apples. How many apples will each student get if distributed equally?
They will get 6 apples each.
To distribute the apples equally, we need to divide the total apples by the number of students.
462/77 = 6
A garden is rectangular, the length of the garden is 33 meters and the total area is 462 square meters. Find the width?
14 meters.
To find the width of the garden, we use the formula,
Area = length × width
462 = 33 × width
To find the value of width, we need to shift 33 to the left side.
462/33 = width
Width = 14.
There are 11 buses and 462 passengers. How many passengers will be in each bus?
Each bus will have 42 passengers.
To find the passengers in each bus, divide the total passengers by the buses.
462/11 = 42
In a school, there are 462 students, and 21 classes. How many students are there in each class?
There are 22 students in each class.
Dividing the students by the total classes, we will get the number of students in each class.
462/21 = 22
462 books need to be arranged in 66 shelves. How many books will go on each shelf?
Each of the shelves has 7 books.
Divide total books by shelves.
462/66 = 7
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.