101 LearnersLast updated on May 26th, 2025
Factors of 731
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 731, how they are used in real life, and tips to learn them quickly.
What are the Factors of 731?
The numbers that divide 731 evenly are known as factors of 731.
A factor of 731 is a number that divides the number without remainder.
The factors of 731 are 1, 17, 43, and 731.
Negative factors of 731: -1, -17, -43, and -731.
Prime factors of 731: 17 and 43.
Prime factorization of 731: 17 × 43.
The sum of factors of 731: 1 + 17 + 43 + 731 = 792.
How to Find Factors of 731?
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 731. Identifying the numbers which are multiplied to get the number 731 is the multiplication method.
Step 1: Multiply 731 by 1, 731 × 1 = 731.
Step 2: Check for other numbers that give 731 after multiplying
17 × 43 = 731
Therefore, the positive factor pairs of 731 are: (1, 731) and (17, 43).
All these factor pairs result in 731.
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 731 by 1, 731 ÷ 1 = 731.
Step 2: Continue dividing 731 by the numbers until the remainder becomes 0.
731 ÷ 1 = 731
731 ÷ 17 = 43
731 ÷ 43 = 17
Therefore, the factors of 731 are: 1, 17, 43, 731.
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 731 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
731 ÷ 17 = 43
43 ÷ 43 = 1
The prime factors of 731 are 17 and 43.
The prime factorization of 731 is: 17 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 731 is divided by 17 to get 43.
Step 2: Now divide 43 by 43 to get 1. Here, 43 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 731 is: 17 × 43.
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 731: (1, 731) and (17, 43).
Negative factor pairs of 731: (-1, -731) and (-17, -43).
Common Mistakes and How to Avoid Them in Factors of 731
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 731, 1 and 731 are also factors.
Factors of 731 Examples
Problem 1
A farmer has 731 apples and wants to pack them equally into boxes of 17 apples each. How many boxes will he need?
He will need 43 boxes.
Explanation
To determine the number of boxes, divide the total apples by the number of apples per box.
731/17 = 43
Problem 2
A rectangular garden has an area of 731 square meters and a length of 43 meters. What is the width of the garden?
17 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 731 = 43 × width
To find the value of width, we need to shift 43 to the left side.
731/43 = width
Width = 17.
Problem 3
There are 731 seats in a theater, and they want to arrange them into rows of 43 seats each. How many rows will there be?
There will be 17 rows.
Explanation
To find the number of rows, divide the total seats by the seats per row.
731/43 = 17
Problem 4
A classroom has 731 students and 17 teachers. How many students will be assigned to each teacher?
Each teacher will have 43 students.
Explanation
Dividing the students by the total teachers, we will get the number of students per teacher.
731/17 = 43
Problem 5
A company has 731 products to distribute equally among 731 stores. How many products will each store receive?
Each store will receive 1 product.
Explanation
Divide total products by stores.
731/731 = 1
FAQs on Factors of 731
1.What are the factors of 731?
2.Mention the prime factors of 731.
3.Is 731 a multiple of 17?
4.Mention the factor pairs of 731?
5.What is the square of 731?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 731?
7.What are some fun ways kids in United Kingdom can practice Factors of 731 with numbers?
8.What role do numbers and Factors of 731 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 731 skills?
Important Glossaries for Factors of 731
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 731 are 1, 17, 43, and 731.
- Prime factors: The factors which are prime numbers. For example, 17 and 43 are prime factors of 731.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 731 is 17 × 43.
- 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 731 are (1, 731) and (17, 43).
- Negative factors: The negative counterparts of the factors of a number. For example, the negative factors of 731 are -1, -17, -43, and -731.
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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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