100 LearnersLast updated on May 26th, 2025
Factors of 1689
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 1689, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1689?
The numbers that divide 1689 evenly are known as factors of 1689.
A factor of 1689 is a number that divides the number without remainder.
The factors of 1689 are 1, 3, 563, and 1689.
Negative factors of 1689: -1, -3, -563, and -1689.
Prime factors of 1689: 3 and 563.
Prime factorization of 1689: 3 × 563.
The sum of factors of 1689: 1 + 3 + 563 + 1689 = 2256
How to Find Factors of 1689?
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 1689. Identifying the numbers which are multiplied to get the number 1689 is the multiplication method.
Step 1: Multiply 1689 by 1, 1689 × 1 = 1689.
Step 2: Check for other numbers that give 1689 after multiplying 3 × 563 = 1689
Therefore, the positive factor pairs of 1689 are: (1, 1689) and (3, 563).
These factor pairs result in 1689.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 1689 by 1, 1689 ÷ 1 = 1689.
Step 2: Continue dividing 1689 by the numbers until the remainder becomes 0.
1689 ÷ 1 = 1689
1689 ÷ 3 = 563
Therefore, the factors of 1689 are: 1, 3, 563, and 1689.
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 1689 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1689 ÷ 3 = 563
563 ÷ 563 = 1
The prime factors of 1689 are 3 and 563.
The prime factorization of 1689 is: 3 × 563.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1689 is divided by 3 to get 563.
Step 2: Then divide 563 by 563 to get 1. Here, 3 and 563 are the prime numbers, and they cannot be divided anymore. So, the prime factorization of 1689 is: 3 × 563.
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 1689: (1, 1689) and (3, 563).
Negative factor pairs of 1689: (-1, -1689) and (-3, -563).
Common Mistakes and How to Avoid Them in Factors of 1689
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 1689, 1 and 1689 is also a factor.
Factors of 1689 Examples
Problem 1
A theater has 3 rows with a total of 1689 seats. How many seats are in each row?
Each row has 563 seats.
Explanation
To find the number of seats in each row, we need to divide the total seats by the number of rows.
1689/3 = 563
Problem 2
A garden has a total of 1689 flowers arranged in 563 rows. How many flowers are in each row?
There are 3 flowers in each row.
Explanation
To find the flowers in each row, we use the formula,
Total flowers = number of rows × flowers per row
1689 = 563 × flowers per row
To find the value of flowers per row, shift 563 to the left side.
1689/563 = flowers per row
Flowers per row = 3.
Problem 3
There are 1689 candies distributed among 1 child. How many candies does the child get?
The child gets 1689 candies.
Explanation
To find the candies for the child, divide the total candies by the number of children.
1689/1 = 1689
Problem 4
A library has 1689 books, and there are 3 shelves. How many books are there on each shelf?
There are 563 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
1689/3 = 563
Problem 5
1689 apples are packed into 563 boxes. How many apples are in each box?
Each box has 3 apples.
Explanation
Divide the total apples by the number of boxes.
1689/563 = 3
FAQs on Factors of 1689
1.What are the factors of 1689?
2.Mention the prime factors of 1689.
3.Is 1689 a multiple of 3?
4.Mention the factor pairs of 1689?
5.What is the square of 1689?
Important Glossaries for Factors of 1689
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1689 are 1, 3, 563, and 1689.
- Prime factors: The factors which are prime numbers. For example, 3 and 563 are prime factors of 1689.
- 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 1689 are (1, 1689) and (3, 563).
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1689 is 3 × 563.
- Divisibility: A number is divisible by another if the remainder is zero when divided. For example, 1689 is divisible by 3.
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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.
