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232 LearnersLast updated on December 17, 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
| Factor Type | Values |
| Positive Factors of 735 | (1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735) |
| Negative Factors of 735 | (-1, -3, -5, -7, -15, -21, -35, -49, -105, -147, -245, -735) |
| Prime Factors of 735 | (3, 5, 7) |
| Prime Factorization of 735 | 3 × 5 × 7² |
| Sum of factors of 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.
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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
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime factors of 735
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.
Prime Factorization of 735
Prime Factorization breaks down the prime factors of 735.
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 Tree of 735
The factor tree is the graphical representation of breaking down any number into prime factors.
Factor Pairs of 735
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:
| Factors | Positive Pair Factors |
| 1 × 735 = 735 | 1, 735 |
| 3 × 245 = 735 | 3, 245 |
| 5 × 147 = 735 | 5, 147 |
| 7 × 105 = 735 | 7, 105 |
| 15 × 49 = 735 | 15, 49 |
| 21 × 35 = 735 | 21, 35 |
Negative factor pairs of 735:
| Factors | Negative Pair Factors |
| −1 × −735 = 735 | −1, −735 |
| −3 × −245 = 735 | −3, −245 |
| −5 × −147 = 735 | −5, −147 |
| −7 × −105 = 735 | −7, −105 |
| −15 × −49 = 735 | −15, −49 |
| −21 × −35 = 735 | −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.
Mistake 2
Missing Negative Factors
We have used to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 735 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 735/2.5 = 294, 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 735 are prime numbers.
For example, 3, 5, and 7 are the prime factors of 735, but it has other factors like 21, 49.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 735 as 3 × 5 × 7² and missing all the key factors.
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
A Walmart store in New York City identifies a billing error while reconciling grocery bills and local sales tax. The accounting system shows a 735 USD adjustment that must be divided into equal whole-dollar corrections across departments. What are all the factors of 735 that represent possible equal splits?
1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
Explanation
To find the factors of 735, start with its prime factorization.
735 = 3 × 5 × 7 × 7
Using all combinations of these prime factors gives every number that divides 735 evenly with no remainder.
Those numbers form the complete list of factors of 735.
Problem 4
In a Boston school science lab, students study pharmacy inventory similar to systems used by CVS. A sample contains 735 mg of a compound that must be divided into equal integer dosage units for testing. Which numbers are factors of 735?
1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
Explanation
A factor is a number that divides 735 exactly without leaving a remainder.
Since 735 = 3 × 5 × 7²,
all valid products of these primes give its factors.
Each value listed divides the total dosage evenly.
Problem 5
An NBA team in Los Angeles (LA) reviews travel expenses after a road game in San Francisco. Based on gas prices per gallon, the team records 735 gallons of fuel usage that must be split evenly across fuel entries. What are all the factors of 735 that allow an exact split?
1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
Explanation
To divide 735 gallons evenly, the number of groups must divide 735 with no remainder.
Using the prime factorization of 735, all possible divisors are identified.
These divisors represent all the valid equal splits.
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 many factors does 735 have?
7.What is the smallest factor of 735?
8.What is the largest factor of 735?
9.Which factors of 735 add up to 13?
10.How many even factors does 735 have?
11.What are the odd factors of 735?
12.What is the sum of all the factors of 735?
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.
