103 LearnersLast updated on May 26th, 2025
Factors of 730
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 730, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 730?
The numbers that divide 730 evenly are known as factors of 730.
A factor of 730 is a number that divides the number without remainder.
The factors of 730 are 1, 2, 5, 10, 73, 146, 365, and 730.
Negative factors of 730: -1, -2, -5, -10, -73, -146, -365, and -730.
Prime factors of 730: 2, 5, and 73.
Prime factorization of 730: 2 × 5 × 73.
The sum of factors of 730: 1 + 2 + 5 + 10 + 73 + 146 + 365 + 730 = 1,332
How to Find Factors of 730?
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 730. Identifying the numbers which are multiplied to get the number 730 is the multiplication method.
Step 1: Multiply 730 by 1, 730 × 1 = 730.
Step 2: Check for other numbers that give 730 after multiplying
2 × 365 = 730
5 × 146 = 730
10 × 73 = 730
Therefore, the positive factor pairs of 730 are: (1, 730), (2, 365), (5, 146), (10, 73).
All these factor pairs result in 730.
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 a whole number as factors. Factors can be calculated by following the simple division method
Step 1: Divide 730 by 1, 730 ÷ 1 = 730.
Step 2: Continue dividing 730 by the numbers until the remainder becomes 0.
730 ÷ 1 = 730
730 ÷ 2 = 365
730 ÷ 5 = 146
730 ÷ 10 = 73
Therefore, the factors of 730 are: 1, 2, 5, 10, 73, 146, 365, 730.
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 730 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
730 ÷ 2 = 365
365 ÷ 5 = 73
73 ÷ 73 = 1
The prime factors of 730 are 2, 5, and 73.
The prime factorization of 730 is: 2 × 5 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 730 is divided by 2 to get 365.
Step 2: Now divide 365 by 5 to get 73.
Step 3: Here, 73 is the smallest prime number that cannot be divided further.
So, the prime factorization of 730 is: 2 × 5 × 73.
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 730: (1, 730), (2, 365), (5, 146), (10, 73).
Negative factor pairs of 730: (-1, -730), (-2, -365), (-5, -146), (-10, -73).
Common Mistakes and How to Avoid Them in Factors of 730
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 730, 1 and 730 are also factors.
Factors of 730 Examples
Problem 1
There are 10 friends and 730 candies. How will they divide it equally?
They will get 73 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
730/10 = 73
Problem 2
A rectangular garden has a length of 146 meters and a total area of 730 square meters. Find the width.
5 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 730 = 146 × width
To find the value of width, we need to shift 146 to the left side.
730/146 = width
Width = 5.
Problem 3
There are 73 bags and 730 apples. How many apples will be in each bag?
Each bag will have 10 apples.
Explanation
To find the apples in each bag, divide the total apples with the bags.
730/73 = 10
Problem 4
In a class, there are 730 students, and 365 groups. How many students are there in each group?
There are 2 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
730/365 = 2
Problem 5
730 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 365 books.
Explanation
Divide total books with shelves.
730/2 = 365
FAQs on Factors of 730
1.What are the factors of 730?
2.Mention the prime factors of 730.
3.Is 730 a multiple of 73?
4.Mention the factor pairs of 730.
5.What is the square of 730?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 730?
7.What are some fun ways kids in United Kingdom can practice Factors of 730 with numbers?
8.What role do numbers and Factors of 730 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 730 skills?
Important Glossary for Factors of 730
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 730 are 1, 2, 5, 10, 73, 146, 365, and 730.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 73 are prime factors of 730.
- 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 730 are (1, 730), (2, 365), etc.
- Multiplication method: A technique used to find factors by identifying pairs of numbers that multiply to give the original number.
- Division method: A technique used to find factors by dividing the number by whole numbers until the remainder is zero.
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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.
