120 LearnersLast updated on May 26th, 2025
Factors of 1921
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1921, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1921?
The numbers that divide 1921 evenly are known as factors of 1921.
A factor of 1921 is a number that divides the number without a remainder.
The factors of 1921 are 1, 11, 17, 121, 187, and 1921.
Negative factors of 1921: -1, -11, -17, -121, -187, and -1921.
Prime factors of 1921: 11 and 17.
Prime factorization of 1921: 11 × 17.
The sum of factors of 1921: 1 + 11 + 17 + 121 + 187 + 1921 = 2258
How to Find Factors of 1921?
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 1921. Identifying the numbers which are multiplied to get the number 1921 is the multiplication method.
Step 1: Multiply 1921 by 1, 1921 × 1 = 1921.
Step 2: Check for other numbers that give 1921 after multiplying
11 × 17 = 1921
Therefore, the positive factor pairs of 1921 are: (1, 1921), (11, 17). 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 1921 by 1, 1921 ÷ 1 = 1921.
Step 2: Continue dividing 1921 by the numbers until the remainder becomes 0.
1921 ÷ 1 = 1921
1921 ÷ 11 = 17
1921 ÷ 17 = 11
Therefore, the factors of 1921 are: 1, 11, 17, 121, 187, and 1921.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1921 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 1921 ÷ 11 = 17 17 ÷ 17 = 1 The prime factors of 1921 are 11 and 17. The prime factorization of 1921 is: 11 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1921 is divided by 11 to get 17.
Step 2: Now, 17 is a prime number and cannot be divided further. So, the prime factorization of 1921 is: 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 1921: (1, 1921), (11, 17).
Negative factor pairs of 1921: (-1, -1921), (-11, -17).
Common Mistakes and How to Avoid Them in Factors of 1921
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 1921, 1 and 1921 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1921 consist of -1, -11, -17, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1921/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1921 are prime numbers.
For example, 11 and 17 are the prime factors of 1921, but it has other factors like 121.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1921 as 11 × 17 and missing all the key factors.
Factors of 1921 Examples
Problem 1
A teacher has 1921 pencils and wants to distribute them evenly among 11 classes. How many pencils will each class receive?
Each class will receive 17 pencils.
Explanation
To divide the pencils equally, we need to divide the total number of pencils by the number of classes.
1921 ÷ 11 = 17
Problem 2
A rectangular garden has a length of 17 meters and an area of 1921 square meters. What is the width of the garden?
The width is 113 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1921 = 17 × width
To find the value of width, we need to divide the area by the length.
1921 ÷ 17 = width
Width = 113
Problem 3
A library has 1921 books and 17 shelves. How many books will be on each shelf?
Each shelf will have 113 books.
Explanation
To find the number of books on each shelf, divide the total number of books by the number of shelves.
1921 ÷ 17 = 113
Problem 4
In a stadium, there are 1921 seats and 121 rows. How many seats are there in each row?
There are 16 seats in each row.
Explanation
Dividing the seats by the number of rows, we will get the number of seats in each row.
1921 ÷ 121 = 16
Problem 5
A batch of 1921 cupcakes needs to be arranged in boxes, each containing 11 cupcakes. How many boxes are needed?
175 boxes are needed.
Explanation
Divide the total cupcakes by the number of cupcakes per box.
1921 ÷ 11 = 175
FAQs on Factors of 1921
1.What are the factors of 1921?
2.Mention the prime factors of 1921.
3.Is 1921 a multiple of 11?
4.Mention the factor pairs of 1921?
5.What is the square of 1921?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 1921?
7.What are some fun ways kids in Indonesia can practice Factors of 1921 with numbers?
8.What role do numbers and Factors of 1921 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 1921 skills?
Important Glossaries for Factors of 1921
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1921 are 1, 11, 17, 121, 187, and 1921.
- Prime factors: The factors which are prime numbers. For example, 11 and 17 are prime factors of 1921.
- 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 1921 are (1, 1921) and (11, 17).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1921 is 11 × 17.
- Negative factors: Factors can also be negative. For example, -1, -11, -17, -121, -187, and -1921 are negative factors of 1921.
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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
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