122 LearnersLast updated on May 26th, 2025
Factors of 527
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 527, how they are used in real life, and tips to learn them quickly.
What are the Factors of 527?
The numbers that divide 527 evenly are known as factors of 527.
A factor of 527 is a number that divides the number without remainder.
The factors of 527 are 1, 17, 31, and 527.
Negative factors of 527: -1, -17, -31, and -527.
Prime factors of 527: 17 and 31.
Prime factorization of 527: 17 × 31.
The sum of factors of 527: 1 + 17 + 31 + 527 = 576
How to Find Factors of 527?
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 527. Identifying the numbers which are multiplied to get the number 527 is the multiplication method.
Step 1: Multiply 527 by 1, 527 × 1 = 527.
Step 2: Check for other numbers that give 527 after multiplying 17 × 31 = 527
Therefore, the positive factor pairs of 527 are: (1, 527), (17, 31).
All these factor pairs result in 527.
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 527 by 1, 527 ÷ 1 = 527.
Step 2: Continue dividing 527 by the numbers until the remainder becomes 0.
527 ÷ 1 = 527
527 ÷ 17 = 31
527 ÷ 31 = 17
Therefore, the factors of 527 are: 1, 17, 31, 527.
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 527 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
527 ÷ 17 = 31
31 ÷ 31 = 1
The prime factors of 527 are 17 and 31.
The prime factorization of 527 is: 17 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 527 is divided by 17 to get 31.
Step 2: 31 is a prime number, so it cannot be divided further. So, the prime factorization of 527 is: 17 × 31.
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 527: (1, 527), (17, 31).
Negative factor pairs of 527: (-1, -527), (-17, -31).
Common Mistakes and How to Avoid Them in Factors of 527
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 word. Always remember to include 1 and the number itself.
For example, in factors of 527, 1 and 527 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 527 consist of -1, -17, 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 527/1.5 = 351.333, 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 527 are prime numbers.
For example, 17 and 31 are the prime factors of 527, but it has other factors like 1, 527.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 527 as 17 × 31 and missing all the key factors.
Factors of 527 Examples
Problem 1
There are 17 teachers and 527 pens. How will they divide them equally?
They will get 31 pens each.
Explanation
To divide the pens equally, we need to divide the total pens with the number of teachers.
527/17 = 31
Problem 2
A garden is rectangular, the length of the garden is 31 meters and the total area is 527 square meters. Find the width?
17 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
527 = 31 × width
To find the value of width, we need to shift 31 to the left side.
527/31 = width
Width = 17.
Problem 3
There are 31 baskets and 527 apples. How many apples will be in each basket?
Each basket will have 17 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
527/31 = 17
Problem 4
In a class, there are 527 students, and 17 groups. How many students are there in each group?
There are 31 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
527/17 = 31
Problem 5
527 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 17 books.
Explanation
Divide total books with shelves.
527/31 = 17
FAQs on Factors of 527
1.What are the factors of 527?
2.Mention the prime factors of 527.
3.Is 527 a multiple of 17?
4.Mention the factor pairs of 527?
5.What is the square of 527?
6.How can children in India use numbers in everyday life to understand Factors of 527?
7.What are some fun ways kids in India can practice Factors of 527 with numbers?
8.What role do numbers and Factors of 527 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 527 skills?
Important Glossaries for Factors of 527
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 527 are 1, 17, 31, and 527.
- Prime factors: The factors which are prime numbers. For example, 17 and 31 are prime factors of 527.
- 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 527 are (1, 527) and (17, 31).
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 527 is 17 × 31.
- Negative factors: Factors that are negative. For example, the negative factors of 527 are -1, -17, -31, -527.
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About BrightChamps in India
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.
