119 LearnersLast updated on May 26th, 2025
Factors of 780
Factors are the numbers that divide any given number evenly without a 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 780, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 780?
The numbers that divide 780 evenly are known as factors of 780.
A factor of 780 is a number that divides the number without remainder.
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, and 780.
Negative factors of 780: -1, -2, -3, -4, -5, -6, -10, -12, -13, -15, -20, -26, -30, -39, -52, -60, -65, -78, -130, -156, -195, -260, -390, and -780.
Prime factors of 780: 2, 3, 5, and 13.
Prime factorization of 780: 2 × 3 × 5 × 13.
The sum of factors of 780: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 13 + 15 + 20 + 26 + 30 + 39 + 52 + 60 + 65 + 78 + 130 + 156 + 195 + 260 + 390 + 780 = 2340
How to Find Factors of 780?
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 780. Identifying the numbers which are multiplied to get the number 780 is the multiplication method.
Step 1: Multiply 780 by 1, 780 × 1 = 780.
Step 2: Check for other numbers that give 780 after multiplying
2 × 390 = 780
3 × 260 = 780
4 × 195 = 780
5 × 156 = 780
6 × 130 = 780
10 × 78 = 780
12 × 65 = 780
13 × 60 = 780
15 × 52 = 780
20 × 39 = 780
26 × 30 = 780
Therefore, the positive factor pairs of 780 are: (1, 780), (2, 390), (3, 260), (4, 195), (5, 156), (6, 130), (10, 78), (12, 65), (13, 60), (15, 52), (20, 39), (26, 30).
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 simple division method
Step 1: Divide 780 by 1, 780 ÷ 1 = 780.
Step 2: Continue dividing 780 by the numbers until the remainder becomes 0.
780 ÷ 1 = 780
780 ÷ 2 = 390
780 ÷ 3 = 260
780 ÷ 4 = 195
780 ÷ 5 = 156
780 ÷ 6 = 130
780 ÷ 10 = 78
780 ÷ 12 = 65
780 ÷ 13 = 60
780 ÷ 15 = 52
780 ÷ 20 = 39
780 ÷ 26 = 30
Therefore, the factors of 780 are: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, and 780.
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 780 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
780 ÷ 2 = 390
390 ÷ 2 = 195
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 780 are 2, 3, 5, and 13.
The prime factorization of 780 is: 2 × 3 × 5 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 780 is divided by 2 to get 390.
Step 2: Now divide 390 by 2 to get 195.
Step 3: Then divide 195 by 3 to get 65.
Step 4: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 780 is: 2 × 3 × 5 × 13.
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 780: (1, 780), (2, 390), (3, 260), (4, 195), (5, 156), (6, 130), (10, 78), (12, 65), (13, 60), (15, 52), (20, 39), (26, 30).
Negative factor pairs of 780: (-1, -780), (-2, -390), (-3, -260), (-4, -195), (-5, -156), (-6, -130), (-10, -78), (-12, -65), (-13, -60), (-15, -52), (-20, -39), (-26, -30).
Common Mistakes and How to Avoid Them in Factors of 780
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 780, 1 and 780 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 780 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 780/1.5 = 520, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 780 are prime numbers.
For instance, 2, 3, 5, and 13 are the prime factors of 780, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 780 as 2 × 3 × 5 × 13 and missing key factors.
Factors of 780 Examples
Problem 1
There are 12 teams and 780 players. How will they be distributed equally?
Each team will have 65 players.
Explanation
To distribute the players equally, we need to divide the total players by the number of teams.
780/12 = 65
Problem 2
A warehouse has a rectangular floor area of 780 square meters. If the length is 39 meters, what is the width?
20 meters.
Explanation
To find the width of the warehouse, we use the formula,
Area = length × width
780 = 39 × width
To find the width, divide the area by the length.
780/39 = width
Width = 20.
Problem 3
There are 26 trucks and 780 packages. How many packages will each truck carry?
Each truck will carry 30 packages.
Explanation
To find the number of packages in each truck, divide the total packages by the number of trucks.
780/26 = 30
Problem 4
In a company, there are 780 employees, and they are divided into 15 departments. How many employees are there in each department?
There are 52 employees in each department.
Explanation
Dividing the employees by the total number of departments, we find the number of employees in each department.
780/15 = 52
Problem 5
780 chairs need to be arranged in 65 rows. How many chairs will go in each row?
Each row will have 12 chairs.
Explanation
Divide the total number of chairs by the number of rows.
780/65 = 12
FAQs on Factors of 780
1.What are the factors of 780?
2.Mention the prime factors of 780.
3.Is 780 a multiple of 13?
4.Mention the factor pairs of 780?
5.What is the square of 780?
6.How can children in Thailand use numbers in everyday life to understand Factors of 780?
7.What are some fun ways kids in Thailand can practice Factors of 780 with numbers?
8.What role do numbers and Factors of 780 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 780 skills?
Important Glossaries for Factors of 780
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, and 780.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 780.
- 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 780 are (1, 780), (2, 390), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number.
- Division method: A method to find factors by dividing the original number by whole numbers, checking if the remainder is zero.
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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.
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