124 LearnersLast updated on June 4th, 2025
Factors of 721
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 721, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 721?
The numbers that divide 721 evenly are known as factors of 721.
A factor of 721 is a number that divides the number without remainder.
The factors of 721 are 1, 7, 103, and 721.
Negative factors of 721: -1, -7, -103, and -721.
Prime factors of 721: 7 and 103.
Prime factorization of 721: 7 × 103.
The sum of factors of 721: 1 + 7 + 103 + 721 = 832
How to Find Factors of 721?
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 721. Identifying the numbers which are multiplied to get the number 721 is the multiplication method.
Step 1: Multiply 721 by 1, 721 × 1 = 721.
Step 2: Check for other numbers that give 721 after multiplying 7 × 103 = 721
Therefore, the positive factor pairs of 721 are: (1, 721) and (7, 103).
All these factor pairs result in 721.
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 721 by 1, 721 ÷ 1 = 721.
Step 2: Continue dividing 721 by the numbers until the remainder becomes 0. 721 ÷ 1 = 721 721 ÷ 7 = 103 721 ÷ 103 = 7
Therefore, the factors of 721 are: 1, 7, 103, 721.
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 721 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
721 ÷ 7 = 103
103 ÷ 103 = 1
The prime factors of 721 are 7 and 103. The prime factorization of 721 is: 7 × 103.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 721 is divided by 7 to get 103.
Step 2: Now divide 103 by 103 to get 1. Here, 103 is a prime number, so it cannot be divided further. So, the prime factorization of 721 is: 7 × 103.
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 721: (1, 721) and (7, 103).
Negative factor pairs of 721: (-1, -721) and (-7, -103).
Common Mistakes and How to Avoid Them in Factors of 721
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 721, 1 and 721 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 721 include -1, -7, -103, and -721.
Mistake 3
Including the Fraction
Children might sometimes mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 721/1.5 ≈ 480.67, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 721 are prime numbers. While 7 and 103 are the prime factors, 1 and 721 are also factors.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 721 as 7 × 103 and missing key factors.
Factors of 721 Examples
Problem 1
There are 7 teams and 721 tasks. How will they divide the tasks equally?
They will get 103 tasks each.
Explanation
To divide the tasks equally, we need to divide the total tasks by the number of teams.
721/7 = 103
Problem 2
A garden is rectangular, the length of the garden is 103 meters and the total area is 721 square meters. Find the width.
7 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
721 = 103 × width
To find the value of width, we need to shift 103 to the left side.
721/103 = width
Width = 7.
Problem 3
There are 721 apples and 103 baskets. How many apples will be in each basket?
Each basket will have 7 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
721/103 = 7
Problem 4
In a class, there are 721 students, and 7 groups. How many students are there in each group?
There are 103 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
721/7 = 103
Problem 5
721 pages need to be arranged in 7 folders. How many pages will go in each folder?
Each of the folders has 103 pages.
Explanation
Divide total pages by folders.
721/7 = 103
FAQs on Factors of 721
1.What are the factors of 721?
2.Mention the prime factors of 721.
3.Is 721 a multiple of 7?
4.Mention the factor pairs of 721.
5.What is the square of 721?
6.How can children in Thailand use numbers in everyday life to understand Factors of 721?
7.What are some fun ways kids in Thailand can practice Factors of 721 with numbers?
8.What role do numbers and Factors of 721 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 721 skills?
Important Glossaries for Factors of 721
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 721 are 1, 7, 103, and 721.
- Prime factors: The factors which are prime numbers. For example, 7 and 103 are prime factors of 721.
- 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 721 are (1, 721) and (7, 103).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 721 is 7 × 103.
- Negative factors: Factors that are negative counterparts of the positive factors. For example, the negative factors of 721 are -1, -7, -103, and -721.
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About BrightChamps in Thailand
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.
