Last updated on May 26th, 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 232, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 232 evenly are known as factors of 232.
A factor of 232 is a number that divides the number without remainder.
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, and 232.
Negative factors of 232: -1, -2, -4, -8, -29, -58, -116, and -232.
Prime factors of 232: 2 and 29.
Prime factorization of 232: 2³ × 29.
The sum of factors of 232: 1 + 2 + 4 + 8 + 29 + 58 + 116 + 232 = 450
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 232. Identifying the numbers which are multiplied to get the number 232 is the multiplication method.
Step 1: Multiply 232 by 1, 232 × 1 = 232.
Step 2: Check for other numbers that give 232 after multiplying:
2 × 116 = 232
4 × 58 = 232
8 × 29 = 232
Therefore, the positive factor pairs of 232 are: (1, 232), (2, 116), (4, 58), (8, 29).
All these factor pairs result in 232.
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 232 by 1,
232 ÷ 1 = 232.
Step 2: Continue dividing 232 by the numbers until the remainder becomes 0.
232 ÷ 1 = 232
232 ÷ 2 = 116
232 ÷ 4 = 58
232 ÷ 8 = 29
Therefore, the factors of 232 are: 1, 2, 4, 8, 29, 58, 116, 232.
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 232 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
232 ÷ 2 = 116
116 ÷ 2 = 58
58 ÷ 2 = 29
29 ÷ 29 = 1
The prime factors of 232 are 2 and 29.
The prime factorization of 232 is: 2³ × 29.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 232 is divided by 2 to get 116.
Step 2: Now divide 116 by 2 to get 58.
Step 3: Then divide 58 by 2 to get 29.
Here, 29 is a prime number that cannot be divided anymore.
So, the prime factorization of 232 is: 2³ × 29.
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 232: (1, 232), (2, 116), (4, 58), and (8, 29).
Negative factor pairs of 232: (-1, -232), (-2, -116), (-4, -58), and (-8, -29).
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 29 students and 232 apples. How will they divide it equally?
They will get 8 apples each.
To divide the apples equally, we need to divide the total apples by the number of students.
232/29 = 8
A rectangular garden has a width of 8 meters and a total area of 232 square meters. Find the length.
29 meters.
To find the length of the garden, we use the formula: Area = length × width
232 = length × 8
To find the value of length, divide 232 by 8.
232/8 = length
Length = 29.
There are 58 oranges and 4 baskets. How many oranges will be in each basket?
Each basket will have 14.5 oranges.
To find the oranges in each basket, divide the total oranges by the baskets.
58/4 = 14.5
In a library, there are 232 books, and each shelf can hold 29 books. How many shelves are needed?
8 shelves are needed.
Dividing the books by the books per shelf gives the number of shelves.
232/29 = 8
232 marbles need to be arranged equally in 4 boxes. How many marbles will go in each box?
Each box will have 58 marbles.
Divide the total marbles by the number of boxes.
232/4 = 58
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.