118 LearnersLast updated on May 26th, 2025
Factors of 1524
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 1524, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1524?
The numbers that divide 1524 evenly are known as factors of 1524.
A factor of 1524 is a number that divides the number without a remainder.
The factors of 1524 are 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, and 1524.
Negative factors of 1524: -1, -2, -3, -4, -6, -12, -127, -254, -381, -508, -762, and -1524.
Prime factors of 1524: 2, 3, and 127. Prime factorization of 1524: 22 × 3 × 127.
The sum of factors of 1524: 1 + 2 + 3 + 4 + 6 + 12 + 127 + 254 + 381 + 508 + 762 + 1524 = 3584
How to Find Factors of 1524?
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 1524. Identifying the numbers which are multiplied to get the number 1524 is the multiplication method.
Step 1: Multiply 1524 by 1, 1524 × 1 = 1524.
Step 2: Check for other numbers that give 1524 after multiplying
2 × 762 = 1524
3 × 508 = 1524
4 × 381 = 1524
6 × 254 = 1524
12 × 127 = 1524
Therefore, the positive factor pairs of 1524 are: (1, 1524), (2, 762), (3, 508), (4, 381), (6, 254), and (12, 127). All these factor pairs result in 1524. 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 a simple division method
Step 1: Divide 1524 by 1, 1524 ÷ 1 = 1524.
Step 2: Continue dividing 1524 by the numbers until the remainder becomes 0.
1524 ÷ 1 = 1524
1524 ÷ 2 = 762
1524 ÷ 3 = 508
1524 ÷ 4 = 381
1524 ÷ 6 = 254
1524 ÷ 12 = 127
Therefore, the factors of 1524 are: 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, and 1524.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1524 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1524 ÷ 2 = 762
762 ÷ 2 = 381
381 ÷ 3 = 127
127 ÷ 127 = 1
The prime factors of 1524 are 2, 3, and 127.
The prime factorization of 1524 is: 22 × 3 × 127.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1524 is divided by 2 to get 762.
Step 2: Now divide 762 by 2 to get 381.
Step 3: Then divide 381 by 3 to get 127. Here, 127 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1524 is: 22 × 3 × 127.
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 1524: (1, 1524), (2, 762), (3, 508), (4, 381), (6, 254), and (12, 127).
Negative factor pairs of 1524: (-1, -1524), (-2, -762), (-3, -508), (-4, -381), (-6, -254), and (-12, -127).
Common Mistakes and How to Avoid Them in Factors of 1524
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1524, 1 and 1524 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 1524 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1524/1.5 = 1016, 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 1524 are prime numbers. For example, 2, 3, and 127 are the prime factors of 1524, but it has other factors like 6, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1524 as 22 × 3 × 127 and missing all the key factors.
Factors of 1524 Examples
Problem 1
There are 6 teams and 762 marbles. How will they distribute them equally?
They will get 127 marbles each.
Explanation
To distribute the marbles equally, we need to divide the total marbles by the number of teams.
762/6 = 127
Problem 2
A garden is rectangular, the width of the garden is 2 meters, and the total area is 762 square meters. Find the length?
381 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
762 = length × 2
To find the value of the length, we need to shift 2 to the left side.
762/2 = length
Length = 381.
Problem 3
There are 4 bins and 508 candies. How many candies will be in each bin?
Each bin will have 127 candies.
Explanation
To find the candies in each bin, divide the total candies by the bins.
508/4 = 127
Problem 4
In a class, there are 12 projects, and 127 groups. How many projects does each group get?
Each group gets 1 project.
Explanation
Dividing the projects by the total groups, we will get the number of projects per group.
127/12 = 1 (with a remainder, but the question implies distribution)
Problem 5
1524 pencils need to be arranged in 6 boxes. How many pencils will go in each box?
Each of the boxes has 254 pencils.
Explanation
Divide total pencils by boxes.
1524/6 = 254
FAQs on Factors of 1524
1.What are the factors of 1524?
2.Mention the prime factors of 1524.
3.Is 1524 a multiple of 4?
4.Mention the factor pairs of 1524?
5.What is the square of 1524?
6.How can children in Canada use numbers in everyday life to understand Factors of 1524?
7.What are some fun ways kids in Canada can practice Factors of 1524 with numbers?
8.What role do numbers and Factors of 1524 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1524 skills?
Important Glossaries for Factor of 1524
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1524 are 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, and 1524.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 127 are prime factors of 1524.
- 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 1524 are (1, 1524), (2, 762), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1524 is 22 × 3 × 127.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1524 is a multiple of 6.
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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
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