118 LearnersLast updated on May 26th, 2025
Factors of 516
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 516, how they are used in real life, and tips to learn them quickly.
What are the Factors of 516?
The numbers that divide 516 evenly are known as factors of 516.
A factor of 516 is a number that divides the number without remainder.
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, and 516.
Negative factors of 516: -1, -2, -3, -4, -6, -12, -43, -86, -129, -172, -258, and -516.
Prime factors of 516: 2, 3, and 43.
Prime factorization of 516: 2² × 3 × 43.
The sum of factors of 516: 1 + 2 + 3 + 4 + 6 + 12 + 43 + 86 + 129 + 172 + 258 + 516 = 1232
How to Find Factors of 516?
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 516. Identifying the numbers which are multiplied to get the number 516 is the multiplication method.
Step 1: Multiply 516 by 1, 516 × 1 = 516.
Step 2: Check for other numbers that give 516 after multiplying
2 × 258 = 516
3 × 172 = 516
4 × 129 = 516
6 × 86 = 516
12 × 43 = 516
Therefore, the positive factor pairs of 516 are: (1, 516), (2, 258), (3, 172), (4, 129), (6, 86), (12, 43).
All these factor pairs result in 516.
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 as whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 516 by 1, 516 ÷ 1 = 516.
Step 2: Continue dividing 516 by the numbers until the remainder becomes 0.
516 ÷ 1 = 516
516 ÷ 2 = 258
516 ÷ 3 = 172
516 ÷ 4 = 129
516 ÷ 6 = 86
516 ÷ 12 = 43
Therefore, the factors of 516 are: 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, and 516.
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 516 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
516 ÷ 2 = 258
258 ÷ 2 = 129
129 ÷ 3 = 43
43 ÷ 43 = 1
The prime factors of 516 are 2, 3, and 43.
The prime factorization of 516 is: 2² × 3 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 516 is divided by 2 to get 258.
Step 2: Now divide 258 by 2 to get 129.
Step 3: Then divide 129 by 3 to get 43. Here, 43 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 516 is: 2² × 3 × 43.
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 516: (1, 516), (2, 258), (3, 172), (4, 129), (6, 86), (12, 43).
Negative factor pairs of 516: (-1, -516), (-2, -258), (-3, -172), (-4, -129), (-6, -86), (-12, -43).
Common Mistakes and How to Avoid Them in Factors of 516
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 516, 1 and 516 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 516 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 5.5 as a factor, because 516/5.5 = 93.8181, 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 516 are prime numbers.
For example, 2, 3, and 43 are the prime factors of 516, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 516 as 2² × 3 × 43 and missing all the key factors.
Factors of 516 Examples
Problem 1
There are 6 friends and 516 candies. How will they divide them equally?
They will get 86 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
516/6 = 86
Problem 2
A field is rectangular, the length of the field is 43 meters and the total area is 516 square meters. Find the width?
12 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
516 = 43 × width
To find the value of width, we need to shift 43 to the left side.
516/43 = width
Width = 12.
Problem 3
There are 43 bags and 516 apples. How many apples will be in each bag?
Each bag will have 12 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
516/43 = 12
Problem 4
In a class, there are 516 students, and 12 groups. How many students are there in each group?
There are 43 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
516/12 = 43
Problem 5
516 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 172 books.
Explanation
Divide total books by shelves.
516/3 = 172
FAQs on Factors of 516
1.What are the factors of 516?
2.Mention the prime factors of 516.
3.Is 516 a multiple of 3?
4.Mention the factor pairs of 516?
5.What is the square of 516?
6.How can children in Qatar use numbers in everyday life to understand Factors of 516?
7.What are some fun ways kids in Qatar can practice Factors of 516 with numbers?
8.What role do numbers and Factors of 516 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 516 skills?
Important Glossaries for Factor of 516
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, and 516.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 43 are prime factors of 516.
- 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 516 are (1, 516), (2, 258), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 516 is 2² × 3 × 43.
- Multiples: The result of multiplying a number by an integer. For example, 516 is a multiple of 3.
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About BrightChamps in Qatar
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.
