102 LearnersLast updated on May 26th, 2025
Factors of 1284
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 1284, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1284?
The numbers that divide 1284 evenly are known as factors of 1284.
A factor of 1284 is a number that divides the number without remainder.
The factors of 1284 are 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, and 1284.
Negative factors of 1284: -1, -2, -3, -4, -6, -12, -107, -214, -321, -428, -642, and -1284.
Prime factors of 1284: 2, 3, and 107.
Prime factorization of 1284: 2² × 3 × 107.
The sum of factors of 1284: 1 + 2 + 3 + 4 + 6 + 12 + 107 + 214 + 321 + 428 + 642 + 1284 = 3024
How to Find Factors of 1284?
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 1284. Identifying the numbers which are multiplied to get the number 1284 is the multiplication method.
Step 1: Multiply 1284 by 1, 1284 × 1 = 1284.
Step 2: Check for other numbers that give 1284 after multiplying
2 × 642 = 1284
3 × 428 = 1284
4 × 321 = 1284
6 × 214 = 1284
12 × 107 = 1284
Therefore, the positive factor pairs of 1284 are: (1, 1284), (2, 642), (3, 428), (4, 321), (6, 214), (12, 107).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
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 1284 by 1, 1284 ÷ 1 = 1284.
Step 2: Continue dividing 1284 by the numbers until the remainder becomes 0.
1284 ÷ 1 = 1284
1284 ÷ 2 = 642
1284 ÷ 3 = 428
1284 ÷ 4 = 321
1284 ÷ 6 = 214
1284 ÷ 12 = 107
Therefore, the factors of 1284 are: 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284.
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 1284 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1284 ÷ 2 = 642
642 ÷ 2 = 321
321 ÷ 3 = 107
107 ÷ 107 = 1
The prime factors of 1284 are 2, 3, and 107.
The prime factorization of 1284 is: 2² × 3 × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1284 is divided by 2 to get 642.
Step 2: Now divide 642 by 2 to get 321.
Step 3: Then divide 321 by 3 to get 107.
Step 4: Divide 107 by 107 to get 1.
Here, 107 is a prime number that cannot be divided anymore.
So, the prime factorization of 1284 is: 2² × 3 × 107.
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 1284: (1, 1284), (2, 642), (3, 428), (4, 321), (6, 214), (12, 107).
Negative factor pairs of 1284: (-1, -1284), (-2, -642), (-3, -428), (-4, -321), (-6, -214), (-12, -107).
Common Mistakes and How to Avoid Them in Factors of 1284
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1284, 1 and 1284 are also factors.
Factors of 1284 Examples
Problem 1
There are 12 teams and 1284 tickets. How will they divide it equally?
They will get 107 tickets each.
Explanation
To divide the tickets equally, we need to divide the total tickets by the number of teams.
1284/12 = 107
Problem 2
A garden is rectangular, the length of the garden is 6 meters and the total area is 1284 square meters. Find the width?
214 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1284 = 6 × width
To find the value of width, we need to shift 6 to the left side.
1284/6 = width
Width = 214.
Problem 3
There are 321 boxes and 1284 apples. How many apples will be in each box?
Each box will have 4 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1284/321 = 4
Problem 4
In an auditorium, there are 642 seats, and 2 sections. How many seats are there in each section?
There are 321 seats in each section.
Explanation
Dividing the seats with the total sections, we will get the number of seats in each section.
1284/2 = 642
Problem 5
1284 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 214 books.
Explanation
Divide total books by shelves.
1284/6 = 214
FAQs on Factors of 1284
1.What are the factors of 1284?
2.Mention the prime factors of 1284.
3.Is 1284 a multiple of 3?
4.Mention the factor pairs of 1284?
5.What is the square of 1284?
Important Glossaries for Factor of 1284
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1284 are 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, and 1284.
- Prime Factors: The factors which are prime numbers. For example, 2, 3, and 107 are prime factors of 1284.
- 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 1284 are (1, 1284), (2, 642), etc.
- Prime Factorization: Expressing a number as the product of its prime factors. For example, 1284 = 2² × 3 × 107.
- Negative Factors: Factors that are negative numbers. For example, the negative factors of 1284 are -1, -2, -3, etc.
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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.
