102 LearnersLast updated on May 26th, 2025
Factors of 1681
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 1681, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1681?
The numbers that divide 1681 evenly are known as factors of 1681.
A factor of 1681 is a number that divides the number without remainder.
The factors of 1681 are 1, 41, and 1681. Negative factors of 1681: -1, -41, and -1681.
Prime factors of 1681: 41.
Prime factorization of 1681: 41².
The sum of factors of 1681: 1 + 41 + 1681 = 1723
How to Find Factors of 1681?
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 1681. Identifying the numbers that are multiplied to get the number 1681 is the multiplication method.
Step 1: Multiply 1681 by 1, 1681 × 1 = 1681.
Step 2: Check for other numbers that give 1681 after multiplying 41 × 41 = 1681
Therefore, the positive factor pairs of 1681 are: (1, 1681) and (41, 41).
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 1681 by 1, 1681 ÷ 1 = 1681.
Step 2: Continue dividing 1681 by the numbers until the remainder becomes 0.
1681 ÷ 1 = 1681
1681 ÷ 41 = 41
Therefore, the factors of 1681 are: 1, 41, 1681.
Prime Factors and Prime Factorization
The factors can be found by dividing with a prime number. 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 1681 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1681 ÷ 41 = 41
41 ÷ 41 = 1
The prime factor of 1681 is 41.
The prime factorization of 1681 is: 41².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1681 is divided by 41 to get 41.
Step 2: Now divide 41 by 41 to get 1. So, the prime factorization of 1681 is: 41².
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 1681: (1, 1681) and (41, 41).
Negative factor pairs of 1681: (-1, -1681) and (-41, -41).
Common Mistakes and How to Avoid Them in Factors of 1681
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1681, 1 and 1681 are also factors.
Factors of 1681 Examples
Problem 1
There are 41 teams and 1681 participants. How will they divide the participants equally among the teams?
They will get 41 participants each.
Explanation
To divide the participants equally, we need to divide the total participants with the number of teams.
1681/41 = 41
Problem 2
A square garden has an area of 1681 square meters. Find the length of one side of the garden.
41 meters.
Explanation
To find the side length of the square garden, we use the formula,
Area = side² 1681 = side²
Take the square root of 1681 to find the side length.
Side = √1681 = 41.
Problem 3
A company has 1681 widgets and needs to package them into boxes, each containing 41 widgets. How many boxes are needed?
41 boxes.
Explanation
To find the number of boxes, divide the total widgets by the number of widgets per box.
1681/41 = 41
Problem 4
A school has 1681 books and wants to distribute them equally among 41 classes. How many books will each class receive?
Each class will receive 41 books.
Explanation
Dividing the books by the total number of classes will give the number of books each class receives.
1681/41 = 41
Problem 5
A concert has 1681 seats, and each row has 41 seats. How many rows are there?
There are 41 rows.
Explanation
Divide the total number of seats by the number of seats per row.
1681/41 = 41
FAQs on Factors of 1681
1.What are the factors of 1681?
2.Mention the prime factors of 1681.
3.Is 1681 a multiple of 41?
4.Mention the factor pairs of 1681?
5.What is the square of 41?
Important Glossaries for Factor of 1681
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1681 are 1, 41, and 1681.
- Prime factors: The factors which are prime numbers. For example, 41 is a prime factor of 1681.
- 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 1681 are (1, 1681) and (41, 41).
- Square number: A number that can be expressed as the product of an integer with itself. For example, 1681 is a square number because it is 41².
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1681 is 41².
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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.
