113 LearnersLast updated on May 26th, 2025
Factors of 517
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 517, how they are used in real life, and tips to learn them quickly.
What are the Factors of 517?
The numbers that divide 517 evenly are known as factors of 517.
A factor of 517 is a number that divides the number without remainder.
The factors of 517 are 1, 11, 47, and 517.
Negative factors of 517: -1, -11, -47, and -517.
Prime factors of 517: 11 and 47.
Prime factorization of 517: 11 × 47.
The sum of factors of 517: 1 + 11 + 47 + 517 = 576
How to Find Factors of 517?
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 517. Identifying the numbers which are multiplied to get the number 517 is the multiplication method.
Step 1: Multiply 517 by 1, 517 × 1 = 517.
Step 2: Check for other numbers that give 517 after multiplying 11 × 47 = 517
Therefore, the positive factor pairs of 517 are: (1, 517) and (11, 47).
All these factor pairs result in 517.
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 517 by 1, 517 ÷ 1 = 517.
Step 2: Continue dividing 517 by the numbers until the remainder becomes 0.
517 ÷ 1 = 517
517 ÷ 11 = 47
517 ÷ 47 = 11
517 ÷ 517 = 1
Therefore, the factors of 517 are: 1, 11, 47, 517.
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 517 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
517 ÷ 11 = 47
47 ÷ 47 = 1
The prime factors of 517 are 11 and 47.
The prime factorization of 517 is: 11 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 517 is divided by 11 to get 47.
Step 2: Now divide 47 by 47 to get 1. Here, 47 is a prime number and cannot be divided further. So, the prime factorization of 517 is: 11 × 47.
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 517: (1, 517) and (11, 47).
Negative factor pairs of 517: (-1, -517) and (-11, -47).
Common Mistakes and How to Avoid Them in Factors of 517
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 517, 1 and 517 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 517 consist of -1, -11, -47, etc.
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 517/1.5 = 344.666..., 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 517 are prime numbers.
For example, 11 and 47 are the prime factors of 517, but it has other factors like 1 and 517.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 517 as 11 × 47 and missing all the key factors.
Factors of 517 Examples
Problem 1
There are 11 groups and 517 candies. How will they divide it equally?
They will get 47 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of groups.
517/11 = 47
Problem 2
A classroom is rectangular, the length of the classroom is 47 meters and the total area is 517 square meters. Find the width.
11 meters.
Explanation
To find the width of the classroom, we use the formula,
Area = length × width
517 = 47 × width
To find the value of width, we need to shift 47 to the left side.
517/47 = width
Width = 11.
Problem 3
There are 47 bags and 517 apples. How many apples will be in each bag?
Each bag will have 11 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
517/47 = 11
Problem 4
In a class, there are 517 students, and 47 groups. How many students are there in each group?
There are 11 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
517/47 = 11
Problem 5
517 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has 47 books.
Explanation
Divide total books by shelves.
517/11 = 47
FAQs on Factors of 517
1.What are the factors of 517?
2.Mention the prime factors of 517.
3.Is 517 a multiple of 11?
4.Mention the factor pairs of 517?
5.What is the square of 517?
Important Glossaries for Factors of 517
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 517 are 1, 11, 47, and 517.
- Prime factors: The factors which are prime numbers. For example, 11 and 47 are prime factors of 517.
- 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 517 are (1, 517) and (11, 47).
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 517 is 11 × 47.
- Negative factors: Factors that are negative counterparts of positive factors. For example, -1, -11, -47, and -517 are negative factors of 517.
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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.
