108 LearnersLast updated on May 26th, 2025
Factors of 1224
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 1224, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1224?
The numbers that divide 1224 evenly are known as factors of 1224. A factor of 1224 is a number that divides the number without remainder. The factors of 1224 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 289, 408, 578, 612, and 1224.
Negative factors of 1224: -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, -289, -408, -578, -612, and -1224.
Prime factors of 1224: 2, 3, and 17.
Prime factorization of 1224: 2³ × 3 × 17².
The sum of factors of 1224: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 + 289 + 408 + 578 + 612 + 1224 = 3774
How to Find Factors of 1224?
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 1224. Identifying the numbers which are multiplied to get the number 1224 is the multiplication method.
Step 1: Multiply 1224 by 1, 1224 × 1 = 1224.
Step 2: Check for other numbers that give 1224 after multiplying
2 × 612 = 1224
3 × 408 = 1224
4 × 306 = 1224
6 × 204 = 1224
8 × 153 = 1224
12 × 102 = 1224
17 × 72 = 1224
24 × 51 = 1224
34 × 36 = 1224
Therefore, the positive factor pairs of 1224 are: (1, 1224), (2, 612), (3, 408), (4, 306), (6, 204), (8, 153), (12, 102), (17, 72), (24, 51), and (34, 36). 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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1224 by 1, 1224 ÷ 1 = 1224.
Step 2: Continue dividing 1224 by the numbers until the remainder becomes 0.
1224 ÷ 1 = 1224
1224 ÷ 2 = 612
1224 ÷ 3 = 408
1224 ÷ 4 = 306
1224 ÷ 6 = 204
1224 ÷ 8 = 153
1224 ÷ 12 = 102
1224 ÷ 17 = 72
1224 ÷ 24 = 51
1224 ÷ 34 = 36
Therefore, the factors of 1224 are: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 289, 408, 578, 612, 1224.
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 1224 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1224 ÷ 2 = 612
612 ÷ 2 = 306
306 ÷ 2 = 153
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 1224 are 2, 3, and 17. The prime factorization of 1224 is: 2³ × 3 × 17².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1224 is divided by 2 to get 612.
Step 2: Now divide 612 by 2 to get 306.
Step 3: Then divide 306 by 2 to get 153.
Step 4: Divide 153 by 3 to get 51. Step 5: Divide 51 by 3 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1224 is: 2³ × 3 × 17².
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 1224: (1, 1224), (2, 612), (3, 408), (4, 306), (6, 204), (8, 153), (12, 102), (17, 72), (24, 51), and (34, 36).
- Negative factor pairs of 1224: (-1, -1224), (-2, -612), (-3, -408), (-4, -306), (-6, -204), (-8, -153), (-12, -102), (-17, -72), (-24, -51), and (-34, -36).
Common Mistakes and How to Avoid Them in Factors of 1224
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 1224, 1 and 1224 are also factors.
Factors of 1224 Examples
Problem 1
There are 68 students and 1224 pencils. How will they distribute them equally?
They will get 18 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
1224/68 = 18
Problem 2
A concert hall can hold 1224 people. If the seating is arranged in 34 rows, how many seats are there per row?
36 seats per row.
Explanation
To find the number of seats per row, use the formula,
Total seats = rows × seats per row
1224 = 34 × seats per row
To find the value of seats per row, divide 1224 by 34.
1224/34 = 36
Problem 3
There are 102 boxes and 1224 toys. How many toys will be in each box?
Each box will have 12 toys.
Explanation
To find the toys in each box, divide the total toys by the number of boxes.
1224/102 = 12
Problem 4
In a school, there are 51 classrooms and 1224 chairs. How many chairs are there in each classroom?
There are 24 chairs in each classroom.
Explanation
Dividing the total chairs by the total classrooms, we will get the number of chairs in each classroom.
1224/51 = 24
Problem 5
1224 books need to be arranged in 8 shelves. How many books will go on each shelf?
Each shelf has 153 books.
Explanation
Divide total books by shelves.
1224/8 = 153
FAQs on Factors of 1224
1.What are the factors of 1224?
2.Mention the prime factors of 1224.
3.Is 1224 a multiple of 4?
4.Mention the factor pairs of 1224?
5.What is the square of 1224?
Important Glossaries for Factors of 1224
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1224 are 1, 2, 3, 4, 6, etc.
- Prime Factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 1224.
- 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 1224 are (1, 1224), (2, 612), etc.
- Multiplication Method: A method to find factors by identifying pairs of numbers that multiply to give the target number.
- Division Method: A method to find factors by dividing the number by whole numbers until the remainder is zero.
Explore More numbers
Previous to Factors of 1224
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.
