100 LearnersLast updated on May 26th, 2025
Factors of 1691
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 1691, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1691?
The numbers that divide 1691 evenly are known as factors of 1691.
A factor of 1691 is a number that divides the number without a remainder.
The factors of 1691 are 1, 13, 130, and 1691.
Negative factors of 1691: -1, -13, -130, and -1691.
Prime factors of 1691: 13 and 130.
Prime factorization of 1691: 13 × 130.
The sum of factors of 1691: 1 + 13 + 130 + 1691 = 1835
How to Find Factors of 1691?
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 1691. Identifying the numbers which are multiplied to get the number 1691 is the multiplication method.
Step 1: Multiply 1691 by 1, 1691 × 1 = 1691.
Step 2: Check for other numbers that give 1691 after multiplying 13 × 130 = 1691
Therefore, the positive factor pairs of 1691 are: (1, 1691), (13, 130).
All these factor pairs result in 1691.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1691 by 1, 1691 ÷ 1 = 1691.
Step 2: Continue dividing 1691 by the numbers until the remainder becomes 0.
1691 ÷ 1 = 1691
1691 ÷ 13 = 130
Therefore, the factors of 1691 are: 1, 13, 130, 1691.
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 1691 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1691 ÷ 13 = 130
130 ÷ 13 = 10
The prime factors of 1691 are 13 and 130.
The prime factorization of 1691 is: 13 × 130.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1691 is divided by 13 to get 130.
Step 2: Now divide 130 by 13 to get 10. Here, 10 is the product of primes, which cannot be divided anymore. So, the prime factorization of 1691 is: 13 × 130.
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 1691: (1, 1691), (13, 130).
Negative factor pairs of 1691: (-1, -1691), (-13, -130).
Common Mistakes and How to Avoid Them in Factors of 1691
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 1691, 1 and 1691 is also a factor.
Factors of 1691 Examples
Problem 1
There are 13 teams and 1691 balls. How will they divide it equally?
They will get 130 balls each.
Explanation
To divide the balls equally, we need to divide the total balls with the number of teams.
1691/13 = 130
Problem 2
A plot is rectangular, the length of the plot is 13 meters and the total area is 1691 square meters. Find the width?
130 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1691 = 13 × width
To find the value of width, we need to shift 13 to the left side.
1691/13 = width
Width = 130.
Problem 3
There are 130 boxes and 1691 marbles. How many marbles will be in each box?
Each box will have 13 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
1691/130 = 13
Problem 4
In an auditorium, there are 1691 seats, and 13 sections. How many seats are there in each section?
There are 130 seats in each section.
Explanation
Dividing the seats with the total sections, we will get the number of seats in each section.
1691/13 = 130
Problem 5
1691 books need to be arranged in 13 shelves. How many books will go on each shelf?
Each of the shelves has 130 books.
Explanation
Divide total books with shelves.
1691/13 = 130
FAQs on Factors of 1691
1.What are the factors of 1691?
2.Mention the prime factors of 1691.
3.Is 1691 a multiple of 13?
4.Mention the factor pairs of 1691?
5.What is the square of 1691?
Important Glossaries for Factor of 1691
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1691 are 1, 13, 130, and 1691.
- Prime factors: The factors which are prime numbers. For example, 13 and 130 are prime factors of 1691.
- 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 1691 are (1, 1691) and (13, 130).
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1691 is 13 × 130.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the target number. For example, using the multiplication method to find factors of 1691 involves pairing numbers like 13 × 130.
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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.
