123 LearnersLast updated on May 26th, 2025
Factors of 1716
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 1716, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1716?
The numbers that divide 1716 evenly are known as factors of 1716.
A factor of 1716 is a number that divides the number without a remainder.
The factors of 1716 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 858, and 1716.
Negative factors of 1716: -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -27, -36, -39, -52, -54, -78, -108, -117, -156, -234, -351, -468, -702, -858, and -1716.
Prime factors of 1716: 2, 3, and 13.
Prime factorization of 1716: 2² × 3² × 13 × 11.
The sum of factors of 1716: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 13 + 18 + 26 + 27 + 36 + 39 + 52 + 54 + 78 + 108 + 117 + 156 + 234 + 351 + 468 + 702 + 858 + 1716 = 5355
How to Find Factors of 1716?
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 1716. Identifying the numbers which are multiplied to get the number 1716 is the multiplication method.
Step 1: Multiply 1716 by 1, 1716 × 1 = 1716.
Step 2: Check for other numbers that give 1716 after multiplying
2 × 858 = 1716
3 × 572 = 1716
4 × 429 = 1716
6 × 286 = 1716
9 × 190 = 1716
12 × 143 = 1716
13 × 132 = 1716
18 × 95 = 1716
26 × 66 = 1716
27 × 63 = 1716
36 × 47 = 1716
Therefore, the positive factor pairs of 1716 are: (1, 1716), (2, 858), (3, 572), (4, 429), (6, 286), (9, 190), (12, 143), (13, 132), (18, 95), (26, 66), (27, 63), and (36, 47).
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 a simple division method
Step 1: Divide 1716 by 1, 1716 ÷ 1 = 1716.
Step 2: Continue dividing 1716 by the numbers until the remainder becomes 0.
1716 ÷ 1 = 1716
1716 ÷ 2 = 858
1716 ÷ 3 = 572
1716 ÷ 4 = 429
1716 ÷ 6 = 286
1716 ÷ 9 = 190
1716 ÷ 12 = 143
1716 ÷ 13 = 132
1716 ÷ 18 = 95
1716 ÷ 26 = 66
1716 ÷ 27 = 63
1716 ÷ 36 = 47
Therefore, the factors of 1716 are: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 858, 1716.
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 1716 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1716 ÷ 2 = 858
858 ÷ 2 = 429
429 ÷ 3 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1
The prime factors of 1716 are 2, 3, 11, and 13.
The prime factorization of 1716 is: 2² × 3 × 11 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1716 is divided by 2 to get 858.
Step 2: Now divide 858 by 2 to get 429.
Step 3: Then divide 429 by 3 to get 143.
Step 4: Divide 143 by 11 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1716 is: 2² × 3 × 11 × 13.
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 1716: (1, 1716), (2, 858), (3, 572), (4, 429), (6, 286), (9, 190), (12, 143), (13, 132), (18, 95), (26, 66), (27, 63), and (36, 47).
Negative factor pairs of 1716: (-1, -1716), (-2, -858), (-3, -572), (-4, -429), (-6, -286), (-9, -190), (-12, -143), (-13, -132), (-18, -95), (-26, -66), (-27, -63), and (-36, -47).
Common Mistakes and How to Avoid Them in Factors of 1716
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1716, 1 and 1716 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1716 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1716/1.5 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 1716 are prime numbers.
For example, 2, 3, and 13 are the prime factors of 1716, but it has other factors like 4, 6, and so on.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1716 as 2² × 3 × 11 × 13 and missing all the key factors.
Factors of 1716 Examples
Problem 1
A factory has 1716 machines, and the manager wants to divide them equally into 6 departments. How many machines will each department get?
Each department will get 286 machines.
Explanation
To divide the machines equally, we need to divide the total number of machines by the number of departments.
1716/6 = 286
Problem 2
A field is rectangular, the length of the field is 39 meters and the total area is 1716 square meters. Find the width?
44 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1716 = 39 × width
To find the value of width, we need to shift 39 to the left side.
1716/39 = width
Width = 44.
Problem 3
There are 18 buses and 1716 passengers. How many passengers will be in each bus?
Each bus will have 95 passengers.
Explanation
To find the passengers in each bus, divide the total number of passengers with the buses.
1716/18 = 95
Problem 4
In a class, there are 1716 students, and 13 groups. How many students are there in each group?
There are 132 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1716/13 = 132
Problem 5
1716 books need to be arranged in 27 shelves. How many books will go on each shelf?
Each shelf will have 63 books.
Explanation
Divide the total books by the shelves.
1716/27 = 63
FAQs on Factors of 1716
1.What are the factors of 1716?
2.Mention the prime factors of 1716.
3.Is 1716 a multiple of 12?
4.Mention the factor pairs of 1716?
5.What is the square of 1716?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1716?
7.What are some fun ways kids in Qatar can practice Factors of 1716 with numbers?
8.What role do numbers and Factors of 1716 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1716 skills?
Important Glossaries for Factors of 1716
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1716 are 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 11, and 13 are prime factors of 1716.
- 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 1716 are (1, 1716), (2, 858), etc.
- Prime factorization: Expressing a number as the product of its prime factors, as 1716 = 2² × 3 × 11 × 13.
- Multiples: Numbers that can be obtained by multiplying the original number by an integer. For example, 1716 is a multiple of 12.
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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.
