100 LearnersLast updated on May 26th, 2025
Factors of 735
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 735, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 735?
The numbers that divide 735 evenly are known as factors of 735.
A factor of 735 is a number that divides the number without remainder.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735.
Negative factors of 735: -1, -3, -5, -7, -15, -21, -35, -49, -105, -147, -245, and -735.
Prime factors of 735: 3, 5, and 7.
Prime factorization of 735: 3 × 5 × 7².
The sum of factors of 735: 1 + 3 + 5 + 7 + 15 + 21 + 35 + 49 + 105 + 147 + 245 + 735 = 1368
How to Find Factors of 735?
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 735. Identifying the numbers that are multiplied to get the number 735 is the multiplication method.
Step 1: Multiply 735 by 1, 735 × 1 = 735.
Step 2: Check for other numbers that give 735 after multiplying
3 × 245 = 735
5 × 147 = 735
7 × 105 = 735
15 × 49 = 735
21 × 35 = 735
Therefore, the positive factor pairs of 735 are: (1, 735), (3, 245), (5, 147), (7, 105), (15, 49), (21, 35).
All these factor pairs result in 735.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 735 by 1, 735 ÷ 1 = 735.
Step 2: Continue dividing 735 by the numbers until the remainder becomes 0.
735 ÷ 1 = 735
735 ÷ 3 = 245
735 ÷ 5 = 147
735 ÷ 7 = 105
735 ÷ 15 = 49
735 ÷ 21 = 35
Therefore, the factors of 735 are: 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
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 735 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 735 are 3, 5, and 7.
The prime factorization of 735 is: 3 × 5 × 7².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 735 is divided by 3 to get 245.
Step 2: Now divide 245 by 5 to get 49.
Step 3: Then divide 49 by 7 to get 7. Here, 7 is the smallest prime number, which cannot be divided anymore.
So, the prime factorization of 735 is: 3 × 5 × 7².
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 735: (1, 735), (3, 245), (5, 147), (7, 105), (15, 49), (21, 35).
Negative factor pairs of 735: (-1, -735), (-3, -245), (-5, -147), (-7, -105), (-15, -49), (-21, -35).
Common Mistakes and How to Avoid Them in Factors of 735
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 735, 1 and 735 is also a factor.
Factors of 735 Examples
Problem 1
There are 7 students and 735 candies. How will they divide it equally?
They will get 105 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
735/7 = 105
Problem 2
A rectangular garden has a length of 35 meters and a total area of 735 square meters. Find the width?
21 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 735 = 35 × width
To find the value of width, we need to shift 35 to the left side.
735/35 = width
Width = 21.
Problem 3
There are 245 apples and 5 baskets. How many apples will be in each basket?
Each basket will have 49 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
245/5 = 49
Problem 4
In a conference, there are 735 participants, and 15 groups. How many participants are there in each group?
There are 49 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
735/15 = 49
Problem 5
735 books need to be arranged in 35 shelves. How many books will go on each shelf?
Each of the shelves has 21 books.
Explanation
Divide total books with shelves.
735/35 = 21
FAQs on Factors of 735
1.What are the factors of 735?
2.Mention the prime factors of 735.
3.Is 735 a multiple of 5?
4.Mention the factor pairs of 735?
5.What is the square of 735?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 735?
7.What are some fun ways kids in United Kingdom can practice Factors of 735 with numbers?
8.What role do numbers and Factors of 735 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 735 skills?
Important Glossaries for Factors of 735
- Factors: The numbers that divide a given number without leaving a remainder are called factors. For example, the factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 735.
- 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 735 are (1, 735), (3, 245), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 735 is 3 × 5 × 7².
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 735 is a multiple of 5.
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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.
