127 LearnersLast updated on May 26th, 2025
Factors of 528
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 528, how they are used in real life, and tips to learn them quickly.
What are the Factors of 528?
The numbers that divide 528 evenly are known as factors of 528.
A factor of 528 is a number that divides the number without a remainder.
The factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528.
Negative factors of 528: -1, -2, -3, -4, -6, -8, -11, -12, -16, -22, -24, -33, -44, -48, -66, -88, -132, -176, -264, and -528.
Prime factors of 528: 2, 3, and 11.
Prime factorization of 528: 24 × 3 × 11.
The sum of factors of 528: 1 + 2 + 3 + 4 + 6 + 8 + 11 + 12 + 16 + 22 + 24 + 33 + 44 + 48 + 66 + 88 + 132 + 176 + 264 + 528 = 1488
How to Find Factors of 528?
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 528. Identifying the numbers which are multiplied to get the number 528 is the multiplication method.
Step 1: Multiply 528 by 1, 528 × 1 = 528.
Step 2: Check for other numbers that give 528 after multiplying
2 × 264 = 528
3 × 176 = 528
4 × 132 = 528
6 × 88 = 528
8 × 66 = 528
11 × 48 = 528
12 × 44 = 528
16 × 33 = 528
22 × 24 = 528
Therefore, the positive factor pairs of 528 are: (1, 528), (2, 264), (3, 176), (4, 132), (6, 88), (8, 66), (11, 48), (12, 44), (16, 33), (22, 24).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 528 by 1, 528 ÷ 1 = 528.
Step 2: Continue dividing 528 by the numbers until the remainder becomes 0.
528 ÷ 1 = 528
528 ÷ 2 = 264
528 ÷ 3 = 176
528 ÷ 4 = 132
528 ÷ 6 = 88
528 ÷ 8 = 66
528 ÷ 11 = 48
528 ÷ 12 = 44
528 ÷ 16 = 33
528 ÷ 22 = 24
Therefore, the factors of 528 are: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 528 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
528 ÷ 2 = 264
264 ÷ 2 = 132
132 ÷ 2 = 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 528 are 2, 3, and 11.
The prime factorization of 528 is: 24 × 3 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 528 is divided by 2 to get 264.
Step 2: Now divide 264 by 2 to get 132.
Step 3: Then divide 132 by 2 to get 66.
Step 4: Divide 66 by 2 to get 33.
Step 5: Divide 33 by 3 to get 11.Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 528 is: 24 × 3 × 11.
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 528: (1, 528), (2, 264), (3, 176), (4, 132), (6, 88), (8, 66), (11, 48), (12, 44), (16, 33), (22, 24).
Negative factor pairs of 528: (-1, -528), (-2, -264), (-3, -176), (-4, -132), (-6, -88), (-8, -66), (-11, -48), (-12, -44), (-16, -33), (-22, -24).
Common Mistakes and How to Avoid Them in Factors of 528
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 528, 1 and 528 is also a factor.
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 528 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 528/1.5 = 352, 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 528 are prime numbers.
For example, 2, 3, and 11 are the prime factors of 528, but it has other factors like 4, 8, 24, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 528 as 24 × 3 × 11 and missing all the key factors.
Factors of 528 Examples
Problem 1
There are 12 friends and 528 candies. How will they divide it equally?
They will get 44 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
528/12 = 44
Problem 2
A rectangular plot has a length of 22 meters and the total area is 528 square meters. Find the width.
24 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
528 = 22 × width
To find the value of width, we need to shift 22 to the left side.
528/22 = width
Width = 24.
Problem 3
There are 66 boxes and 528 marbles. How many marbles will be in each box?
Each box will have 8 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
528/66 = 8
Problem 4
In a class, there are 528 students, and 11 groups. How many students are there in each group?
There are 48 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
528/11 = 48
Problem 5
528 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has 48 books.
Explanation
Divide total books with shelves.
528/11 = 48
FAQs on Factors of 528
1.What are the factors of 528?
2.Mention the prime factors of 528.
3.Is 528 a multiple of 3?
4.Mention the factor pairs of 528?
5.What is the square of 528?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 528?
7.What are some fun ways kids in Bahrain can practice Factors of 528 with numbers?
8.What role do numbers and Factors of 528 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 528 skills?
Important Glossaries for Factors of 528
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 528.
- 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 528 are (1, 528), (2, 264), etc.
- Prime factorization: Breaking down a number into its prime number components. For example, the prime factorization of 528 is 24 × 3 × 11.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 528 is a multiple of 2, 3, and 11.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 528
About BrightChamps in Bahrain
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.
