100 LearnersLast updated on May 26th, 2025
Factors of 1780
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 1780, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1780?
The numbers that divide 1780 evenly are known as factors of 1780.
A factor of 1780 is a number that divides the number without remainder.
The factors of 1780 are 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, and 1780.
Negative factors of 1780: -1, -2, -4, -5, -10, -20, -89, -178, -356, -445, -890, and -1780.
Prime factors of 1780: 2, 5, and 89.
Prime factorization of 1780: 2² × 5 × 89.
The sum of factors of 1780: 1 + 2 + 4 + 5 + 10 + 20 + 89 + 178 + 356 + 445 + 890 + 1780 = 3780
How to Find Factors of 1780?
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 1780. Identifying the numbers which are multiplied to get the number 1780 is the multiplication method.
Step 1: Multiply 1780 by 1, 1780 × 1 = 1780.
Step 2: Check for other numbers that give 1780 after multiplying:
2 × 890 = 1780
4 × 445 = 1780
5 × 356 = 1780
10 × 178 = 1780
20 × 89 = 1780
Therefore, the positive factor pairs of 1780 are: (1, 1780), (2, 890), (4, 445), (5, 356), (10, 178), (20, 89).
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 the simple division method:
Step 1: Divide 1780 by 1, 1780 ÷ 1 = 1780.
Step 2: Continue dividing 1780 by the numbers until the remainder becomes 0.
1780 ÷ 1 = 1780
1780 ÷ 2 = 890
1780 ÷ 4 = 445
1780 ÷ 5 = 356
1780 ÷ 10 = 178
1780 ÷ 20 = 89
Therefore, the factors of 1780 are: 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780.
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 1780 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1780 ÷ 2 = 890
890 ÷ 2 = 445
445 ÷ 5 = 89
89 ÷ 89 = 1
The prime factors of 1780 are 2, 5, and 89.
The prime factorization of 1780 is: 2² × 5 × 89.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1780 is divided by 2 to get 890.
Step 2: Now divide 890 by 2 to get 445.
Step 3: Then divide 445 by 5 to get 89.
Here, 89 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1780 is: 2² × 5 × 89.
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 1780: (1, 1780), (2, 890), (4, 445), (5, 356), (10, 178), and (20, 89).
Negative factor pairs of 1780: (-1, -1780), (-2, -890), (-4, -445), (-5, -356), (-10, -178), and (-20, -89).
Common Mistakes and How to Avoid Them in Factors of 1780
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1780, 1 and 1780 are also factors.
Factors of 1780 Examples
Problem 1
There are 10 teams and 1780 trophies. How will they divide them equally?
They will get 178 trophies each.
Explanation
To divide the trophies equally, we need to divide the total trophies by the number of teams.
1780/10 = 178
Problem 2
A garden is rectangular, the length of the garden is 20 meters and the total area is 1780 square meters. Find the width?
89 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1780 = 20 × width
To find the value of width, we need to shift 20 to the left side.
1780/20 = width
Width = 89.
Problem 3
There are 356 candies and 1780 wrappers. How many wrappers will be used for each candy?
Each candy will have 5 wrappers.
Explanation
To find the wrappers for each candy, divide the total wrappers by the candies.
1780/356 = 5
Problem 4
In a sports competition, there are 1780 participants and 5 event sections. How many participants are there in each section?
There are 356 participants in each section.
Explanation
Dividing the participants by the total sections, we will get the number of participants in each section.
1780/5 = 356
Problem 5
1780 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves has 178 books.
Explanation
Divide total books by shelves.
1780/10 = 178
FAQs on Factors of 1780
1.What are the factors of 1780?
2.Mention the prime factors of 1780.
3.Is 1780 a multiple of 4?
4.Mention the factor pairs of 1780?
5.What is the square of 1780?
6.How can children in United States use numbers in everyday life to understand Factors of 1780?
7.What are some fun ways kids in United States can practice Factors of 1780 with numbers?
8.What role do numbers and Factors of 1780 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1780 skills?
Important Glossaries for Factor of 1780
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1780 are 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, and 1780.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 89 are prime factors of 1780.
- 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 1780 are (1, 1780), (2, 890), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1780 is 2² × 5 × 89.
- Divisibility: A concept that determines whether a number can be divided by another number without a remainder. For example, 1780 is divisible by 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
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