107 LearnersLast updated on May 26th, 2025
Factors of 1233
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 1233, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1233?
The numbers that divide 1233 evenly are known as factors of 1233. A factor of 1233 is a number that divides the number without a remainder. The factors of 1233 are 1, 3, 7, 21, 59, 177, 411, and 1233.
Negative factors of 1233: -1, -3, -7, -21, -59, -177, -411, and -1233.
Prime factors of 1233: 3, 7, and 59.
Prime factorization of 1233: 3 × 7 × 59.
The sum of factors of 1233: 1 + 3 + 7 + 21 + 59 + 177 + 411 + 1233 = 1912
How to Find Factors of 1233?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1233. Identifying the numbers which are multiplied to get the number 1233 is the multiplication method.
Step 1: Multiply 1233 by 1, 1233 × 1 = 1233.
Step 2: Check for other numbers that give 1233 after multiplying
3 × 411 = 1233
7 × 177 = 1233
21 × 59 = 1233
Therefore, the positive factor pairs of 1233 are: (1, 1233), (3, 411), (7, 177), (21, 59). All these factor pairs result in 1233. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1233 by 1, 1233 ÷ 1 = 1233.
Step 2: Continue dividing 1233 by the numbers until the remainder becomes 0.
1233 ÷ 1 = 1233
1233 ÷ 3 = 411
1233 ÷ 7 = 177
1233 ÷ 21 = 59
Therefore, the factors of 1233 are: 1, 3, 7, 21, 59, 177, 411, 1233.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1233 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1233 ÷ 3 = 411
411 ÷ 3 = 137
137 ÷ 7 = 19
19 ÷ 19 = 1
The prime factors of 1233 are 3, 7, and 59. The prime factorization of 1233 is: 3 × 7 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1233 is divided by 3 to get 411.
Step 2: Now divide 411 by 3 to get 137.
Step 3: Then divide 137 by 7 to get 19.
Step 4: Divide 19 by 19 to get 1. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1233 is: 3 × 7 × 59.
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 1233: (1, 1233), (3, 411), (7, 177), and (21, 59).
- Negative factor pairs of 1233: (-1, -1233), (-3, -411), (-7, -177), and (-21, -59).
Common Mistakes and How to Avoid Them in Factors of 1233
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every word. Always remember to include 1 and the number itself. For example, in factors of 1233, 1 and 1233 are also factors.
Factors of 1233 Examples
Problem 1
There are 3 baskets and 1233 apples. How will they divide them equally?
They will get 411 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets.
1233/3 = 411
Problem 2
A plot of land is rectangular, the length of the plot is 21 meters, and the total area is 1233 square meters. Find the width?
59 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1233 = 21 × width
To find the value of width, we need to shift 21 to the left side.
1233/21 = width
Width = 59.
Problem 3
There are 177 packages and 1233 items. How many items will be in each package?
Each package will have 7 items.
Explanation
To find the items in each package, divide the total items with the packages.
1233/177 = 7
Problem 4
In a conference, there are 1233 attendees, and 7 rooms. How many attendees are there in each room?
There are 177 attendees in each room.
Explanation
Dividing the attendees with the total rooms, we will get the number of attendees in each room.
1233/7 = 177
Problem 5
1233 tickets need to be distributed in 3 booths. How many tickets will go to each booth?
Each booth has 411 tickets.
Explanation
Divide total tickets with booths.
1233/3 = 411
FAQs on Factors of 1233
1.What are the factors of 1233?
2.Mention the prime factors of 1233.
3.Is 1233 a multiple of 7?
4.Mention the factor pairs of 1233?
5.What is the square of 1233?
Important Glossaries for Factor of 1233
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1233 are 1, 3, 7, 21, 59, 177, 411, and 1233.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 59 are prime factors of 1233.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1233 are (1, 1233), (3, 411), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1233 is 3 × 7 × 59.
- Multiple: A number that can be divided by another number without a remainder. For example, 1233 is a multiple of 3, 7, and 59.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
