118 LearnersLast updated on May 26th, 2025
Factors of 725
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 725, how they are used in real life, and tips to learn them quickly.
What are the Factors of 725?
The numbers that divide 725 evenly are known as factors of 725.
A factor of 725 is a number that divides the number without remainder.
The factors of 725 are 1, 5, 145, and 725.
Negative factors of 725: -1, -5, -145, and -725.
Prime factors of 725: 5 and 29.
Prime factorization of 725: 5 × 145 or 5 × 29.
The sum of factors of 725: 1 + 5 + 145 + 725 = 876
How to Find Factors of 725?
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 725. Identifying the numbers which are multiplied to get the number 725 is the multiplication method.
Step 1: Multiply 725 by 1, 725 × 1 = 725.
Step 2: Check for other numbers that give 725 after multiplying
5 × 145 = 725
Therefore, the positive factor pairs of 725 are: (1, 725) and (5, 145).
All these factor pairs result in 725.
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 725 by 1, 725 ÷ 1 = 725.
Step 2: Continue dividing 725 by the numbers until the remainder becomes 0.
725 ÷ 1 = 725
725 ÷ 5 = 145
725 ÷ 145 = 5
Therefore, the factors of 725 are: 1, 5, 145, 725.
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 725 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
725 ÷ 5 = 145
145 ÷ 5 = 29
29 ÷ 29 = 1
The prime factors of 725 are 5 and 29.
The prime factorization of 725 is: 5 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 725 is divided by 5 to get 145.
Step 2: Now divide 145 by 5 to get 29.
Here, 29 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 725 is: 5 × 29.
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 725: (1, 725) and (5, 145).
Negative factor pairs of 725: (-1, -725) and (-5, -145).
Common Mistakes and How to Avoid Them in Factors of 725
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 725, 1 and 725 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 725 include -1, -5, -145, 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 725/1.5 = 483.333, and it 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 725 are prime numbers.
For example, 5 and 29 are the prime factors of 725, but it has other factors like 145.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 725 as 5 × 145 and missing all the key factors.
Factors of 725 Examples
Problem 1
There are 5 teachers and 725 students. How will they divide the students equally among themselves?
They will get 145 students each.
Explanation
To divide the students equally, we need to divide the total students by the number of teachers.
725/5 = 145
Problem 2
A rectangular room has a length of 145 meters and the total area is 725 square meters. Find the width?
5 meters.
Explanation
To find the width of the room, we use the formula,
Area = length × width
725 = 145 × width
To find the value of the width, we need to shift 145 to the left side.
725/145 = width
Width = 5.
Problem 3
There are 29 boxes and 725 marbles. How many marbles will be in each box?
Each box will have 25 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
725/29 = 25
Problem 4
In a workshop, there are 725 tools, and 145 toolkits. How many tools should each toolkit contain?
Each toolkit should contain 5 tools.
Explanation
Dividing the tools by the total toolkits, we will get the number of tools in each toolkit.
725/145 = 5
Problem 5
725 candies need to be distributed among 145 children. How many candies will each child get?
Each child will get 5 candies.
Explanation
Divide total candies by the number of children.
725/145 = 5
FAQs on Factors of 725
1.What are the factors of 725?
2.Mention the prime factors of 725.
3.Is 725 a multiple of 5?
4.Mention the factor pairs of 725?
5.What is the square of 725?
6.How can children in United States use numbers in everyday life to understand Factors of 725?
7.What are some fun ways kids in United States can practice Factors of 725 with numbers?
8.What role do numbers and Factors of 725 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 725 skills?
Important Glossaries for Factors of 725
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 725 are 1, 5, 145, and 725.
- Prime factors: The factors which are prime numbers. For example, 5 and 29 are prime factors of 725.
- 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 725 are (1, 725) and (5, 145).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 725 is 5 × 29.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, to find factors of 725, identify pairs like (5, 145).
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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.
