116 LearnersLast updated on May 26th, 2025
Factors of 705
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 705, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 705?
The numbers that divide 705 evenly are known as factors of 705.
A factor of 705 is a number that divides the number without remainder.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, and 705.
Negative factors of 705: -1, -3, -5, -15, -47, -141, -235, and -705.
Prime factors of 705: 3, 5, and 47.
Prime factorization of 705: 3 × 5 × 47.
The sum of factors of 705: 1 + 3 + 5 + 15 + 47 + 141 + 235 + 705 = 1,152
How to Find Factors of 705?
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 705. Identifying the numbers which are multiplied to get the number 705 is the multiplication method.
Step 1: Multiply 705 by 1, 705 × 1 = 705.
Step 2: Check for other numbers that give 705 after multiplying
3 × 235 = 705
5 × 141 = 705
15 × 47 = 705
Therefore, the positive factor pairs of 705 are: (1, 705), (3, 235), (5, 141), and (15, 47).
All these factor pairs result in 705. 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 705 by 1, 705 ÷ 1 = 705.
Step 2: Continue dividing 705 by the numbers until the remainder becomes 0.
705 ÷ 1 = 705
705 ÷ 3 = 235
705 ÷ 5 = 141
705 ÷ 15 = 47
Therefore, the factors of 705 are: 1, 3, 5, 15, 47, 141, 235, 705.
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 705 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
705 ÷ 3 = 235
235 ÷ 5 = 47
47 ÷ 47 = 1
The prime factors of 705 are 3, 5, and 47.
The prime factorization of 705 is: 3 × 5 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 705 is divided by 3 to get 235.
Step 2: Now divide 235 by 5 to get 47.
Step 3: Here, 47 is a prime number, that cannot be divided anymore.
So, the prime factorization of 705 is: 3 × 5 × 47.
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 705: (1, 705), (3, 235), (5, 141), and (15, 47).
Negative factor pairs of 705: (-1, -705), (-3, -235), (-5, -141), and (-15, -47).
Common Mistakes and How to Avoid Them in Factors of 705
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 705, 1 and 705 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 705 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor because 705/2.5 = 282, 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 705 are prime numbers.
For example, 3, 5, and 47 are the prime factors of 705, but it has other factors like 15, 141.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 705 as 3 × 5 × 47 and missing all the key factors.
Factors of 705 Examples
Problem 1
There are 3 teams and 705 points. How will they divide it equally?
They will get 235 points each.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
705/3 = 235
Problem 2
A garden is rectangular, the length of the garden is 47 meters and the total area is 705 square meters. Find the width?
15 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
705 = 47 × width
To find the value of width, we need to shift 47 to the left side.
705/47 = width
Width = 15.
Problem 3
There are 5 boxes and 705 marbles. How many marbles will be in each box?
Each box will have 141 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
705/5 = 141
Problem 4
In a school, there are 705 students, and 47 classes. How many students are there in each class?
There are 15 students in each class.
Explanation
Dividing the students with the total classes, we will get the number of students in each class.
705/47 = 15
Problem 5
705 chairs need to be arranged in 5 rows. How many chairs will go in each row?
Each of the rows has 141 chairs.
Explanation
Divide total chairs with rows.
705/5 = 141
FAQs on Factors of 705
1.What are the factors of 705?
2.Mention the prime factors of 705.
3.Is 705 a multiple of 15?
4.Mention the factor pairs of 705?
5.What is the square of 705?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 705?
7.What are some fun ways kids in Vietnam can practice Factors of 705 with numbers?
8.What role do numbers and Factors of 705 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 705 skills?
Important Glossaries for Factors of 705
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 705 are 1, 3, 5, 15, 47, 141, 235, and 705.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 47 are prime factors of 705.
- 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 705 are (1, 705), (3, 235), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 705 is 3 × 5 × 47.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 705 is a multiple of 15.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 705
About BrightChamps in Vietnam
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.
