119 LearnersLast updated on May 26th, 2025
Factors of 529
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 529, how they are used in real life, and tips to learn them quickly.
What are the Factors of 529?
The numbers that divide 529 evenly are known as factors of 529.
A factor of 529 is a number that divides the number without remainder.
The factors of 529 are 1, 23, and 529.
Negative factors of 529: -1, -23, and -529.
Prime factors of 529: 23.
Prime factorization of 529: 23 × 23 or 23².
The sum of factors of 529: 1 + 23 + 529 = 553
How to Find Factors of 529?
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 529. Identifying the numbers which are multiplied to get the number 529 is the multiplication method.
Step 1: Multiply 529 by 1, 529 × 1 = 529.
Step 2: Check for other numbers that give 529 after multiplying 23 × 23 = 529
Therefore, the positive factor pairs of 529 are: (1, 529) and (23, 23).
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 529 by 1, 529 ÷ 1 = 529.
Step 2: Continue dividing 529 by the numbers until the remainder becomes 0.
529 ÷ 1 = 529
529 ÷ 23 = 23
Therefore, the factors of 529 are: 1, 23, and 529.
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 529 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
529 ÷ 23 = 23
23 ÷ 23 = 1
The prime factor of 529 is 23.
The prime factorization of 529 is: 23 × 23 or 23².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 529 is divided by 23 to get 23.
Step 2: Now, divide 23 by 23 to get 1. Here, 23 is the smallest prime number, and it cannot be divided anymore. So, the prime factorization of 529 is: 23 × 23 or 23².
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 529: (1, 529) and (23, 23).
Negative factor pairs of 529: (-1, -529) and (-23, -23).
Common Mistakes and How to Avoid Them in Factors of 529
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
People 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 529, 1 and 529 are also factors.
Mistake 2
Missing Negative Factors
We have commonly mentioned positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 529 include -1, -23, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 529/1.5 = 352.666, 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 529 are prime numbers. The prime factor of 529 is 23, but it has other factors like 1 and 529.
Mistake 5
Mistake in Factorization
People might skip steps in factorization and end up writing wrong factors.
For example, not recognizing 529 as 23 × 23 and missing key factors.
Factors of 529 Examples
Problem 1
There are 23 friends and 529 candies. How will they divide it equally?
They will get 23 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
529/23 = 23
Problem 2
A square field has an area of 529 square meters. What is the side length of the field?
23 meters.
Explanation
To find the side length of a square, we take the square root of the area.
Side length = √529 = 23
Problem 3
There are 1,058 marbles and they need to be divided into 2 boxes. How many marbles will be in each box?
Each box will have 529 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1,058/2 = 529
Problem 4
In a class, there are 529 students, and they need to be divided into 23 groups. How many students are there in each group?
There are 23 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
529/23 = 23
Problem 5
529 books need to be arranged in 23 shelves. How many books will go on each shelf?
Each of the shelves has 23 books.
Explanation
Divide total books by shelves.
529/23 = 23
FAQs on Factors of 529
1.What are the factors of 529?
2.Mention the prime factors of 529.
3.Is 529 a multiple of 23?
4.Mention the factor pairs of 529?
5.What is the square of 23?
Important Glossaries for Factor of 529
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 529 are 1, 23, and 529.
- Prime factors: The factors which are prime numbers. For example, 23 is a prime factor of 529.
- 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 529 are (1, 529) and (23, 23).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 529 is 23 × 23 or 23².
- Square number: A number that is the square of an integer. For example, 529 is a square number, being 23².
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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.
