120 LearnersLast updated on May 26th, 2025
Factors of 1523
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1523, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1523?
The numbers that divide 1523 evenly are known as factors of 1523.
A factor of 1523 is a number that divides the number without remainder.
The factors of 1523 are 1, 1523.
Negative factors of 1523: -1, -1523.
Prime factors of 1523: 1523.
Prime factorization of 1523: 1523 × 1.
The sum of factors of 1523: 1 + 1523 = 1524
How to Find Factors of 1523?
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 1523. Identifying the numbers which are multiplied to get the number 1523 is the multiplication method.
Step 1: Multiply 1523 by 1, 1523 × 1 = 1523.
Therefore, the positive factor pair of 1523 is: (1, 1523).
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 1523 by 1, 1523 ÷ 1 = 1523.
Step 2: Divide 1523 by 1523, 1523 ÷ 1523 = 1.
Therefore, the factors of 1523 are: 1, 1523.
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 1523 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1523 is a prime number itself, so it cannot be factored further.
The prime factorization of 1523 is: 1523 × 1.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. Since 1523 is a prime number, there is no further breakdown. The prime factorization of 1523 is: 1523 × 1.
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 pair of 1523: (1, 1523).
Negative factor pair of 1523: (-1, -1523).
Common Mistakes and How to Avoid Them in Factors of 1523
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 1523, 1 and 1523 are also factors.
Mistake 2
Missing Negative Factors
We have used to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1523 include -1 and -1523.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1523/1.5 does not result in 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 1523 are prime numbers. 1523 itself is a prime factor, but not all numbers are prime.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not realizing that 1523 is a prime number and cannot be broken down further.
Factors of 1523 Examples
Problem 1
There are 1523 apples and 1 person. How will the person receive the apples?
They will receive all 1523 apples.
Explanation
To distribute the apples, we divide the total apples by the number of people.
1523/1 = 1523
Problem 2
A farmer has a plot of land with an area of 1523 square meters. If the length of the plot is 1 meter, what is the width?
1523 meters.
Explanation
To find the width of the plot, we use the formula, Area = length × width
1523 = 1 × width
Width = 1523
Problem 3
There are 1523 units of a product and 1 box. How many units will be in the box?
The box will contain all 1523 units.
Explanation
To find out how many units go into each box, divide the total units by the number of boxes.
1523/1 = 1523
Problem 4
A library has 1523 books and 1 shelf. How many books will go on each shelf?
All 1523 books will go on the shelf.
Explanation
Divide the total books by the number of shelves.
1523/1 = 1523
Problem 5
There are 1 group and 1523 candies. How many candies does the group get?
The group gets all 1523 candies.
Explanation
Divide total candies by the number of groups.
1523/1 = 1523
FAQs on Factors of 1523
1.What are the factors of 1523?
2.Mention the prime factors of 1523.
3.Is 1523 a multiple of 2?
4.Mention the factor pairs of 1523?
5.What is the square of 1523?
Important Glossaries for Factors of 1523
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1523 are 1 and 1523.
- Prime factors: The factors which are prime numbers. For example, 1523 itself is a prime factor.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 1523 is (1, 1523).
- Prime number: A number that has no divisors other than 1 and itself. For example, 1523 is a prime number.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
