119 LearnersLast updated on May 26th, 2025
Factors of 765
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 765, how they are used in real life, and tips to learn them quickly.
What are the Factors of 765?
The numbers that divide 765 evenly are known as factors of 765.
A factor of 765 is a number that divides the number without remainder.
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765.
Negative factors of 765: -1, -3, -5, -9, -15, -17, -45, -51, -85, -153, -255, and -765.
Prime factors of 765: 3, 5, and 17.
Prime factorization of 765: 3 × 5 × 17.
The sum of factors of 765: 1 + 3 + 5 + 9 + 15 + 17 + 45 + 51 + 85 + 153 + 255 + 765 = 1404
How to Find Factors of 765?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 765. Identifying the numbers that are multiplied to get the number 765 is the multiplication method.
Step 1: Multiply 765 by 1, 765 × 1 = 765.
Step 2: Check for other numbers that give 765 after multiplying
3 × 255 = 765
5 × 153 = 765
9 × 85 = 765
15 × 51 = 765
17 × 45 = 765
Therefore, the positive factor pairs of 765 are: (1, 765), (3, 255), (5, 153), (9, 85), (15, 51), (17, 45).
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 765 by 1, 765 ÷ 1 = 765.
Step 2: Continue dividing 765 by the numbers until the remainder becomes 0.
765 ÷ 1 = 765
765 ÷ 3 = 255
765 ÷ 5 = 153
765 ÷ 9 = 85
765 ÷ 15 = 51
765 ÷ 17 = 45
Therefore, the factors of 765 are: 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
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 765 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
765 ÷ 3 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 765 are 3, 5, and 17.
The prime factorization of 765 is: 3 × 5 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 765 is divided by 3 to get 255.
Step 2: Now divide 255 by 3 to get 85.
Step 3: Then divide 85 by 5 to get 17.
Here, 17 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 765 is: 3 × 5 × 17.
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 765: (1, 765), (3, 255), (5, 153), (9, 85), (15, 51), and (17, 45).
Negative factor pairs of 765: (-1, -765), (-3, -255), (-5, -153), (-9, -85), (-15, -51), and (-17, -45).
Common Mistakes and How to Avoid Them in Factors of 765
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 765, 1 and 765 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 765 consist of -1, -3, -5, 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 765/1.5 = 510, but 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 765 are prime numbers.
For example, 3, 5, and 17 are the prime factors of 765, but it has other factors like 9, 15.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not breaking 765 as 3 × 5 × 17 and missing all the key factors.
Factors of 765 Examples
Problem 1
There are 9 workers and 765 bricks. How will they divide it equally?
They will get 85 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks by the number of workers.
765/9 = 85
Problem 2
A garden is rectangular, the length of the garden is 15 meters, and the total area is 765 square meters. Find the width?
51 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
765 = 15 × width
To find the value of width, we need to shift 15 to the left side.
765/15 = width
Width = 51.
Problem 3
There are 17 volunteers and 765 flyers. How many flyers will each volunteer get?
Each volunteer will get 45 flyers.
Explanation
To find the flyers for each volunteer, divide the total flyers by the volunteers.
765/17 = 45
Problem 4
In a class, there are 765 students, and 3 buses. How many students are there in each bus?
There are 255 students in each bus.
Explanation
Dividing the students by the total buses, we will get the number of students in each bus.
765/3 = 255
Problem 5
765 pages need to be printed in 5 batches. How many pages will be printed in each batch?
Each batch will have 153 pages.
Explanation
Divide total pages by batches.
765/5 = 153
FAQs on Factors of 765
1.What are the factors of 765?
2.Mention the prime factors of 765.
3.Is 765 a multiple of 9?
4.Mention the factor pairs of 765?
5.What is the square of 765?
6.How can children in Thailand use numbers in everyday life to understand Factors of 765?
7.What are some fun ways kids in Thailand can practice Factors of 765 with numbers?
8.What role do numbers and Factors of 765 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 765 skills?
Important Glossaries for Factor of 765
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 765 are 1, 3, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 17 are prime factors of 765.
- 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 765 are (1, 765), (3, 255), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 765 is 3 × 5 × 17.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the target number. For example, using multiplication to find factors of 765.
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About BrightChamps in Thailand
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.
