126 LearnersLast updated on June 9th, 2025
Factors of 1484
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 1484, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1484?
The numbers that divide 1484 evenly are known as factors of 1484.
A factor of 1484 is a number that divides the number without a remainder.
The factors of 1484 are 1, 2, 4, 7, 14, 28, 53, 106, 212, 371, 742, and 1484.
Negative factors of 1484: -1, -2, -4, -7, -14, -28, -53, -106, -212, -371, -742, and -1484.
Prime factors of 1484: 2, 7, and 53.
Prime factorization of 1484: 22 × 7 × 53.
The sum of factors of 1484: 1 + 2 + 4 + 7 + 14 + 28 + 53 + 106 + 212 + 371 + 742 + 1484 = 3024
How to Find Factors of 1484?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1484. Identifying the numbers which are multiplied to get the number 1484 is the multiplication method.
Step 1: Multiply 1484 by 1, 1484 × 1 = 1484.
Step 2: Check for other numbers that give 1484 after multiplying:
2 × 742 = 1484
4 × 371 = 1484
7 × 212 = 1484
14 × 106 = 1484
28 × 53 = 1484
Therefore, the positive factor pairs of 1484 are: (1, 1484), (2, 742), (4, 371), (7, 212), (14, 106), (28, 53).
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 1484 by 1, 1484 ÷ 1 = 1484.
Step 2: Continue dividing 1484 by the numbers until the remainder becomes 0.
1484 ÷ 1 = 1484
1484 ÷ 2 = 742
1484 ÷ 4 = 371
1484 ÷ 7 = 212
1484 ÷ 14 = 106
1484 ÷ 28 = 53
Therefore, the factors of 1484 are: 1, 2, 4, 7, 14, 28, 53, 106, 212, 371, 742, 1484.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1484 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1484 ÷ 2 = 742
742 ÷ 2 = 371
371 ÷ 7 = 53
53 ÷ 53 = 1
The prime factors of 1484 are 2, 7, and 53.
The prime factorization of 1484 is: 22 × 7 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1484 is divided by 2 to get 742.
Step 2: Now divide 742 by 2 to get 371.
Step 3: Then divide 371 by 7 to get 53. Here, 53 is a prime number that cannot be divided anymore. So, the prime factorization of 1484 is: 22 × 7 × 53.
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 1484: (1, 1484), (2, 742), (4, 371), (7, 212), (14, 106), and (28, 53).
Negative factor pairs of 1484: (-1, -1484), (-2, -742), (-4, -371), (-7, -212), (-14, -106), and (-28, -53).
Common Mistakes and How to Avoid Them in Factors of 1484
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1484, 1 and 1484 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1484 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1484/1.5 = 989.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1484 are prime numbers. For example, 2, 7, and 53 are the prime factors of 1484, but it has other factors like 4, 28.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, Not breaking 1484 as 22 × 7 × 53 and missing all the key factors.
Factors of 1484 Examples
Problem 1
There are 14 people and 1484 marbles. How will they divide them equally?
They will get 106 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of people.
1484/14 = 106
Problem 2
A rectangular yard has a length of 53 meters and a total area of 1484 square meters. Find the width.
28 meters.
Explanation
To find the width of the yard, we use the formula, Area = length × width
1484 = 53 × width
To find the value of width, we need to shift 53 to the left side.
1484/53 = width
Width = 28.
Problem 3
There are 28 containers and 1484 liters of water. How many liters will be in each container?
Each container will have 53 liters.
Explanation
To find the water in each container, divide the total liters by the number of containers.
1484/28 = 53
Problem 4
In a class, there are 1484 students and 53 groups. How many students are there in each group?
There are 28 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1484/53 = 28
Problem 5
1484 books need to be arranged in 53 shelves. How many books will go on each shelf?
Each of the shelves has 28 books.
Explanation
Divide total books by shelves.
1484/53 = 28
FAQs on Factors of 1484
1.What are the factors of 1484?
2.Mention the prime factors of 1484.
3.Is 1484 a multiple of 4?
4.Mention the factor pairs of 1484.
5.What is the square of 1484?
Important Glossaries for Factor of 1484
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1484 are 1, 2, 4, 7, 14, 28, 53, 106, 212, 371, 742, and 1484.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 53 are prime factors of 1484.
- 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 1484 are (1, 1484), (2, 742), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1484 is 22 × 7 × 53.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, in finding factors of 1484, pairs like (2, 742) are found by multiplication.
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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.
