100 LearnersLast updated on May 26th, 2025
Factors of 1683
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 1683, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1683?
The numbers that divide 1683 evenly are known as factors of 1683.
A factor of 1683 is a number that divides the number without a remainder.
The factors of 1683 are 1, 3, 11, 33, 51, 153, 561, and 1683.
Negative factors of 1683: -1, -3, -11, -33, -51, -153, -561, and -1683.
Prime factors of 1683: 3 and 11.
Prime factorization of 1683: 3 × 11 × 51.
The sum of factors of 1683: 1 + 3 + 11 + 33 + 51 + 153 + 561 + 1683 = 2496
How to Find Factors of 1683?
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 1683. Identifying the numbers which are multiplied to get the number 1683 is the multiplication method.
Step 1: Multiply 1683 by 1, 1683 × 1 = 1683.
Step 2: Check for other numbers that give 1683 after multiplying
3 × 561 = 1683
11 × 153 = 1683
33 × 51 = 1683
Therefore, the positive factor pairs of 1683 are: (1, 1683), (3, 561), (11, 153), (33, 51).
All these factor pairs result in 1683.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1683 by 1, 1683 ÷ 1 = 1683.
Step 2: Continue dividing 1683 by the numbers until the remainder becomes 0.
1683 ÷ 1 = 1683
1683 ÷ 3 = 561
1683 ÷ 11 = 153
1683 ÷ 33 = 51
Therefore, the factors of 1683 are: 1, 3, 11, 33, 51, 153, 561, 1683.
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 1683 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1683 ÷ 3 = 561
561 ÷ 3 = 187
187 ÷ 11 = 17
17 ÷ 17 = 1
The prime factors of 1683 are 3, 11, and 17.
The prime factorization of 1683 is: 3 × 11 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1683 is divided by 3 to get 561.
Step 2: Now divide 561 by 3 to get 187.
Step 3: Then divide 187 by 11 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1683 is: 3 × 11 × 17.
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 1683: (1, 1683), (3, 561), (11, 153), and (33, 51).
Negative factor pairs of 1683: (-1, -1683), (-3, -561), (-11, -153), and (-33, -51).
Common Mistakes and How to Avoid Them in Factors of 1683
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 1683, 1 and 1683 are also factors.
Factors of 1683 Examples
Problem 1
There are 17 teams and 1683 points. How will they divide it equally among themselves?
They will get 99 points each.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
1683/17 = 99
Problem 2
A garden is rectangular, the length of the garden is 33 meters and the total area is 1683 square meters. Find the width?
51 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1683 = 33 × width
To find the value of width, we need to shift 33 to the left side.
1683/33 = width
Width = 51.
Problem 3
There are 153 baskets and 1683 apples. How many apples will be in each basket?
Each basket will have 11 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
1683/153 = 11
Problem 4
In a sports event, there are 33 groups and 1683 participants. How many participants are there in each group?
There are 51 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
1683/33 = 51
Problem 5
1683 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 561 books.
Explanation
Divide total books with shelves.
1683/3 = 561
FAQs on Factors of 1683
1.What are the factors of 1683?
2.Mention the prime factors of 1683.
3.Is 1683 a multiple of 11?
4.Mention the factor pairs of 1683?
5.What is the square of 1683?
Important Glossaries for Factors of 1683
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1683 are 1, 3, 11, 33, 51, 153, 561, and 1683.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 17 are prime factors of 1683.
- 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 1683 are (1, 1683), (3, 561), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1683 is 3 × 11 × 17.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find factors of 1683.
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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.
