102 LearnersLast updated on May 26th, 2025
Factors of 1687
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 1687, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1687?
The numbers that divide 1687 evenly are known as factors of 1687.
A factor of 1687 is a number that divides the number without remainder.
The factors of 1687 are 1, 29, 58, 59, 87, 171, 493, 1687.
Negative factors of 1687: -1, -29, -58, -59, -87, -171, -493, -1687.
Prime factors of 1687: 29 and 59.
Prime factorization of 1687: 29 × 59.
The sum of factors of 1687: 1 + 29 + 58 + 59 + 87 + 171 + 493 + 1687 = 2585
How to Find Factors of 1687?
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 1687. Identifying the numbers which are multiplied to get the number 1687 is the multiplication method.
Step 1: Multiply 1687 by 1, 1687 × 1 = 1687.
Step 2: Check for other numbers that give 1687 after multiplying
29 × 58 = 1687
59 × 29 = 1687
Therefore, the positive factor pairs of 1687 are: (1, 1687), (29, 58), (59, 29).
All these factor pairs result in 1687.
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 the simple division method
Step 1: Divide 1687 by 1, 1687 ÷ 1 = 1687.
Step 2: Continue dividing 1687 by the numbers until the remainder becomes 0.
1687 ÷ 1 = 1687
1687 ÷ 29 = 58
1687 ÷ 59 = 29
Therefore, the factors of 1687 are: 1, 29, 58, 59, 87, 171, 493, 1687.
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 1687 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1687 ÷ 29 = 58
58 ÷ 29 = 2
2 ÷ 2 = 1
The prime factors of 1687 are 29 and 59.
The prime factorization of 1687 is: 29 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1687 is divided by 29 to get 58.
Step 2: Now divide 58 by 29 to get 2.
Step 3: Divide 2 by 2 to get 1. Here, 29 and 59 are the smallest prime numbers that cannot be divided anymore. So, the prime factorization of 1687 is: 29 × 59.
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 1687: (1, 1687), (29, 58), (59, 29).
Negative factor pairs of 1687: (-1, -1687), (-29, -58), (-59, -29).
Common Mistakes and How to Avoid Them in Factors of 1687
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 1687, 1 and 1687 are also factors.
Factors of 1687 Examples
Problem 1
There are 29 students and 1687 pencils. How will they divide them equally?
They will get 58 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
1687/29 = 58
Problem 2
A rectangular garden has a length of 29 meters and a total area of 1687 square meters. Find the width.
58 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1687 = 29 × width
To find the value of width, we need to shift 29 to the left side.
1687/29 = width
Width = 58.
Problem 3
There are 87 boxes and 1687 apples. How many apples will be in each box?
Each box will have 19 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1687/87 = 19
Problem 4
In a school, there are 1687 students, and 59 classes. How many students are there in each class?
There are 29 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
1687/59 = 29
Problem 5
1687 books need to be arranged in 29 shelves. How many books will go on each shelf?
Each of the shelves has 58 books.
Explanation
Divide the total books by the shelves.
1687/29 = 58
FAQs on Factors of 1687
1.What are the factors of 1687?
2.Mention the prime factors of 1687.
3.Is 1687 a multiple of 29?
4.Mention the factor pairs of 1687?
5.What is the square of 1687?
Important Glossaries for Factor of 1687
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1687 are 1, 29, 58, 59, 87, 171, 493, 1687.
- Prime factors: The factors which are prime numbers. For example, 29 and 59 are prime factors of 1687.
- 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 1687 are (1, 1687), (29, 58), etc.
- Multiplication Method: A method used to find factors by identifying pairs of numbers that multiply to give the original number.
- Division Method: A method used to find factors by dividing the number by integers until the remainder is zero.
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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.
