101 LearnersLast updated on May 26th, 2025
Factors of 1682
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 1682, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1682?
The numbers that divide 1682 evenly are known as factors of 1682.
A factor of 1682 is a number that divides the number without remainder.
The factors of 1682 are 1, 2, 841, and 1682.
Negative factors of 1682: -1, -2, -841, and -1682.
Prime factors of 1682: 2 and 29.
Prime factorization of 1682: 2 × 29².
The sum of factors of 1682: 1 + 2 + 841 + 1682 = 2526
How to Find Factors of 1682?
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 1682. Identifying the numbers which are multiplied to get the number 1682 is the multiplication method.
Step 1: Multiply 1682 by 1, 1682 × 1 = 1682.
Step 2: Check for other numbers that give 1682 after multiplying 2 × 841 = 1682
Therefore, the positive factor pairs of 1682 are: (1, 1682) and (2, 841).
All these factor pairs result in 1682.
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 1682 by 1, 1682 ÷ 1 = 1682.
Step 2: Continue dividing 1682 by the numbers until the remainder becomes 0.
1682 ÷ 1 = 1682
1682 ÷ 2 = 841
Therefore, the factors of 1682 are: 1, 2, 841, and 1682.
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 1682 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1682 ÷ 2 = 841
841 ÷ 29 = 29
29 ÷ 29 = 1
The prime factors of 1682 are 2 and 29.
The prime factorization of 1682 is: 2 × 29².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1682 is divided by 2 to get 841.
Step 2: Now divide 841 by 29 to get 29. Here, 29 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1682 is: 2 × 29².
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 1682: (1, 1682) and (2, 841).
Negative factor pairs of 1682: (-1, -1682) and (-2, -841).
Common Mistakes and How to Avoid Them in Factors of 1682
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 1682, 1 and 1682 are also factors.
Factors of 1682 Examples
Problem 1
There are 2 teams and 1682 participants. How will they divide the participants equally?
Each team will have 841 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1682/2 = 841
Problem 2
A rectangular garden has a length of 2 meters and a total area of 1682 square meters. Find the width.
841 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1682 = 2 × width
To find the value of width, we need to shift 2 to the left side.
1682/2 = width
Width = 841.
Problem 3
There are 841 boxes and 1682 apples. How many apples will be in each box?
Each box will have 2 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1682/841 = 2
Problem 4
In a conference, there are 1682 attendees, and 29 sessions. How many attendees are there in each session?
There are 58 attendees in each session.
Explanation
Dividing the attendees by the total sessions, we will get the number of attendees in each session. 1682/29 = 58
Problem 5
1682 chairs need to be arranged in 2 rooms. How many chairs will go in each room?
Each of the rooms has 841 chairs.
Explanation
Divide total chairs by rooms.
1682/2 = 841
FAQs on Factors of 1682
1.What are the factors of 1682?
2.Mention the prime factors of 1682.
3.Is 1682 a multiple of 29?
4.Mention the factor pairs of 1682?
5.What is the square of 29?
Important Glossaries for Factors of 1682
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1682 are 1, 2, 841, and 1682.
- Prime factors: The factors which are prime numbers. For example, 2 and 29 are prime factors of 1682.
- 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 1682 are (1, 1682), (2, 841).
- Prime factorization: Breaking down a number into the product of its prime factors. For example, 1682 = 2 × 29².
- Negative factors: Factors that are negative, for example, -1, -2, -841, and -1682 for the number 1682.
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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.
