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 234, how they are used in real life, and tips to learn them quickly.
The numbers that divide 234 evenly are known as factors of 234.
A factor of 234 is a number that divides the number without remainder.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234.
Negative factors of 234: -1, -2, -3, -6, -9, -13, -18, -26, -39, -78, -117, and -234.
Prime factors of 234: 2, 3, and 13.
Prime factorization of 234: 2 × 3² × 13.
The sum of factors of 234: 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 39 + 78 + 117 + 234 = 546.
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 234. Identifying the numbers which are multiplied to get the number 234 is the multiplication method.
Step 1: Multiply 234 by 1, 234 × 1 = 234.
Step 2: Check for other numbers that give 234 after multiplying
2 × 117 = 234
3 × 78 = 234
6 × 39 = 234
9 × 26 = 234
13 × 18 = 234
Therefore, the positive factor pairs of 234 are: (1, 234), (2, 117), (3, 78), (6, 39), (9, 26), (13, 18).
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 the simple division method -
Step 1: Divide 234 by 1, 234 ÷ 1 = 234.
Step 2: Continue dividing 234 by the numbers until the remainder becomes 0.
234 ÷ 1 = 234
234 ÷ 2 = 117
234 ÷ 3 = 78
234 ÷ 6 = 39
234 ÷ 9 = 26
234 ÷ 13 = 18
Therefore, the factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
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 234 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
234 ÷ 2 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 234 are 2, 3, and 13.
The prime factorization of 234 is: 2 × 3² × 13.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 234 is divided by 2 to get 117.
Step 2: Now divide 117 by 3 to get 39.
Step 3: Then divide 39 by 3 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 234 is: 2 × 3² × 13.
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 234: (1, 234), (2, 117), (3, 78), (6, 39), (9, 26), and (13, 18).
Negative factor pairs of 234: (-1, -234), (-2, -117), (-3, -78), (-6, -39), (-9, -26), and (-13, -18).
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 13 teams and 234 trophies. How will they distribute them equally?
They will get 18 trophies each.
To divide the trophies equally, we need to divide the total trophies with the number of teams.
234/13 = 18
A garden is rectangular, the length of the garden is 13 meters and the total area is 234 square meters. Find the width?
18 meters.
To find the width of the garden, we use the formula, Area = length × width
234 = 13 × width
To find the value of width, we need to shift 13 to the left side.
234/13 = width
Width = 18.
There are 6 gift boxes and 234 chocolates. How many chocolates will be in each box?
Each box will have 39 chocolates.
To find the chocolates in each box, divide the total chocolates with the boxes.
234/6 = 39
In a conference, there are 234 participants, and 9 groups. How many participants are there in each group?
There are 26 participants in each group.
Dividing the participants with the total groups, we will get the number of participants in each group.
234/9 = 26
234 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 78 books.
Divide total books with shelves.
234/3 = 78
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.