121 LearnersLast updated on May 26th, 2025
Factors of 1712
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 1712, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1712?
The numbers that divide 1712 evenly are known as factors of 1712.
A factor of 1712 is a number that divides the number without remainder.
The factors of 1712 are 1, 2, 4, 8, 16, 107, 214, 428, 856, and 1712.
Negative factors of 1712: -1, -2, -4, -8, -16, -107, -214, -428, -856, and -1712.
Prime factors of 1712: 2 and 107.
Prime factorization of 1712: 24 ×107.
The sum of factors of 1712: 1 + 2 + 4 + 8 + 16 + 107 + 214 + 428 + 856 + 1712 = 3348.
How to Find Factors of 1712?
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 1712. Identifying the numbers which are multiplied to get the number 1712 is the multiplication method.
Step 1: Multiply 1712 by 1, 1712 × 1 = 1712.
Step 2: Check for other numbers that give 1712 after multiplying
2 × 856 = 1712
4 × 428 = 1712
8 × 214 = 1712
16 × 107 = 1712
Therefore, the positive factor pairs of 1712 are: (1, 1712), (2, 856), (4, 428), (8, 214), (16, 107).
All these factor pairs result in 1712.
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 1712 by 1, 1712 ÷ 1 = 1712.
Step 2: Continue dividing 1712 by the numbers until the remainder becomes 0.
1712 ÷ 1 = 1712
1712 ÷ 2 = 856
1712 ÷ 4 = 428
1712 ÷ 8 = 214
1712 ÷ 16 = 107
Therefore, the factors of 1712 are: 1, 2, 4, 8, 16, 107, 214, 428, 856, 1712.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1712 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1712 ÷ 2 = 856
856 ÷ 2 = 428
428 ÷ 2 = 214
214 ÷ 2 = 107
107 is a prime number.
The prime factors of 1712 are 2 and 107.
The prime factorization of 1712 is: 24 × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1712 is divided by 2 to get 856.
Step 2: Now divide 856 by 2 to get 428.
Step 3: Then divide 428 by 2 to get 214.
Step 4: Divide 214 by 2 to get 107. Here, 107 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1712 is: 24 × 107.
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 1712: (1, 1712), (2, 856), (4, 428), (8, 214), and (16, 107).
Negative factor pairs of 1712: (-1, -1712), (-2, -856), (-4, -428), (-8, -214), and (-16, -107).
Common Mistakes and How to Avoid Them in Factors of 1712
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 1712, 1 and 1712 is also a factor.
Mistake 2
Missing Negative Factors
We often only mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1712 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1712/1.5 = 1141.333, 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 1712 are prime numbers.
For example, 2 and 107 are the prime factors of 1712, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1712 as 24 × 107 and missing all the key factors.
Factors of 1712 Examples
Problem 1
There are 16 students and 1712 pages to be read. How many pages will each student read if divided equally?
Each student will read 107 pages.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
1712/16 = 107
Problem 2
A rectangular garden has a length of 107 meters, and the total area is 1712 square meters. Find the width?
16 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1712 = 107 × width
To find the value of width, we need to shift 107 to the left side.
1712/107 = width
Width = 16.
Problem 3
There are 8 baskets and 1712 apples. How many apples will be in each basket if divided equally?
Each basket will have 214 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1712/8 = 214
Problem 4
In a factory, there are 4 machines that produce 1712 widgets in total. How many widgets does each machine produce?
Each machine produces 428 widgets.
Explanation
Dividing the total widgets by the number of machines will give the number of widgets each machine produces.
1712/4 = 428
Problem 5
1712 books need to be arranged in 2 large shelves. How many books will go on each shelf?
Each of the shelves has 856 books.
Explanation
Divide the total books by the number of shelves.
1712/2 = 856
FAQs on Factors of 1712
1.What are the factors of 1712?
2.Mention the prime factors of 1712.
3.Is 1712 a multiple of 8?
4.Mention the factor pairs of 1712?
5.What is the square of 1712?
6.How can children in United States use numbers in everyday life to understand Factors of 1712?
7.What are some fun ways kids in United States can practice Factors of 1712 with numbers?
8.What role do numbers and Factors of 1712 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1712 skills?
Important Glossaries for Factor of 1712
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1712 are 1, 2, 4, 8, 16, 107, 214, 428, 856, and 1712.
- Prime factors: The factors which are prime numbers. For example, 2 and 107 are prime factors of 1712.
- 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 1712 are (1, 1712), (2, 856), etc.
- Prime factorization: The representation of a number as a product of its prime factors. For example, 24 × 107 is the prime factorization of 1712.
- Division method: A method to find factors by dividing the number by integers to check which divisions result in whole numbers. For example, dividing 1712 by 2 gives 856, a whole number, thus 2 is a factor.
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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
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