Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 9 workers and 765 bricks. How will they divide it equally?
They will get 85 bricks each.
To divide the bricks equally, we need to divide the total bricks by the number of workers.
765/9 = 85
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.
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.
There are 17 volunteers and 765 flyers. How many flyers will each volunteer get?
Each volunteer will get 45 flyers.
To find the flyers for each volunteer, divide the total flyers by the volunteers.
765/17 = 45
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.
Dividing the students by the total buses, we will get the number of students in each bus.
765/3 = 255
765 pages need to be printed in 5 batches. How many pages will be printed in each batch?
Each batch will have 153 pages.
Divide total pages by batches.
765/5 = 153
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.
: She loves to read number jokes and games.