127 LearnersLast updated on May 26th, 2025
Factors of 1421
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 1421, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1421?
The numbers that divide 1421 evenly are known as factors of 1421.
A factor of 1421 is a number that divides the number without remainder.
The factors of 1421 are 1, 13, 109, and 1421.
Negative factors of 1421: -1, -13, -109, and -1421.
Prime factors of 1421: 13 and 109.
Prime factorization of 1421: 13 × 109.
The sum of factors of 1421: 1 + 13 + 109 + 1421 = 1544
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How to Find Factors of 1421?
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 1421. Identifying the numbers that are multiplied to get the number 1421 is the multiplication method.
Step 1: Multiply 1421 by 1, 1421 × 1 = 1421.
Step 2: Check for other numbers that give 1421 after multiplying 13 × 109 = 1421
Therefore, the positive factor pairs of 1421 are: (1, 1421), (13, 109).
All these factor pairs result in 1421.
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 1421 by 1, 1421 ÷ 1 = 1421.
Step 2: Continue dividing 1421 by the numbers until the remainder becomes 0.
1421 ÷ 1 = 1421
1421 ÷ 13 = 109
1421 ÷ 109 = 13
1421 ÷ 1421 = 1
Therefore, the factors of 1421 are: 1, 13, 109, 1421.
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 1421 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1421 ÷ 13 = 109
109 ÷ 109 = 1
The prime factors of 1421 are 13 and 109.
The prime factorization of 1421 is: 13 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1421 is divided by 13 to get 109.
Step 2: Now divide 109 by 109 to get 1. Here, 109 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1421 is: 13 × 109.
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 1421: (1, 1421), (13, 109).
Negative factor pairs of 1421: (-1, -1421), (-13, -109).
Common Mistakes and How to Avoid Them in Factors of 1421
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 1421, 1 and 1421 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1421 consist of -1, -13, -109, and -1421.
Mistake 3
Including the Fraction
Children might sometimes add fractions as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1421/1.5 = 947.333, which 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 1421 are prime numbers.
For example, 13 and 109 are the prime factors of 1421, but it has other factors like 1 and 1421.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 1421 as 13 × 109 and missing all the key factors.
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Factors of 1421 Examples
Problem 1
There are 13 friends and 1421 candies. How will they divide it equally?
They will get 109 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1421/13 = 109
Problem 2
A field is rectangular, the length of the field is 13 meters, and the total area is 1421 square meters. Find the width?
109 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1421 = 13 × width
To find the value of width, we need to shift 13 to the left side.
1421/13 = width
Width = 109.
Problem 3
There are 109 students, and 1421 books. How many books will each student get?
Each student will get 13 books.
Explanation
To find the books for each student, divide the total books by the students.
1421/109 = 13
Problem 4
In a class, there are 1421 students, and 13 groups. How many students are in each group?
There are 109 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1421/13 = 109
Problem 5
1421 apples need to be arranged in 13 baskets. How many apples will go in each basket?
Each basket will have 109 apples.
Explanation
Divide total apples by baskets.
1421/13 = 109
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FAQs on Factors of 1421
1.What are the factors of 1421?
2.Mention the prime factors of 1421.
3.Is 1421 a multiple of 13?
4.Mention the factor pairs of 1421?
5.What is the square of 1421?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1421?
7.What are some fun ways kids in United Kingdom can practice Factors of 1421 with numbers?
8.What role do numbers and Factors of 1421 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1421 skills?
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Important Glossaries for Factor of 1421
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1421 are 1, 13, 109, and 1421.
- Prime factors: The factors which are prime numbers. For example, 13 and 109 are prime factors of 1421.
- 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 1421 are (1, 1421), (13, 109).
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1421 is 13 × 109.
- Negative factors: The negative numbers that divide the given number without leaving a remainder. For example, the negative factors of 1421 are -1, -13, -109, and -1421.
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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.
