131 LearnersLast updated on May 26th, 2025
Factors of 1820
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 1820, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1820?
The numbers that divide 1820 evenly are known as factors of 1820.
A factor of 1820 is a number that divides the number without a remainder. The factors of 1820 are 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 35, 52, 65, 91, 130, 182, 260, 364, 455, 910, and 1820.
Negative factors of 1820: -1, -2, -4, -5, -7, -10, -13, -14, -20, -26, -35, -52, -65, -91, -130, -182, -260, -364, -455, -910, and -1820.
Prime factors of 1820: 2, 5, 7, 13.
Prime factorization of 1820: 2² × 5 × 7 × 13.
The sum of factors of 1820: 1 + 2 + 4 + 5 + 7 + 10 + 13 + 14 + 20 + 26 + 35 + 52 + 65 + 91 + 130 + 182 + 260 + 364 + 455 + 910 + 1820 = 4420
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How to Find Factors of 1820?
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 pairs of numbers that are multiplied to give 1820. Identifying the numbers which are multiplied to get the number 1820 is the multiplication method.
Step 1: Multiply 1820 by 1, 1820 × 1 = 1820.
Step 2: Check for other numbers that give 1820 after multiplying:
2 × 910 = 1820
4 × 455 = 1820
5 × 364 = 1820
7 × 260 = 1820
10 × 182 = 1820
13 × 140 = 1820
14 × 130 = 1820
20 × 91 = 1820
26 × 70 = 1820
35 × 52 = 1820
Therefore, the positive factor pairs of 1820 are: (1, 1820), (2, 910), (4, 455), (5, 364), (7, 260), (10, 182), (13, 140), (14, 130), (20, 91), (26, 70), and (35, 52).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 1820 by 1, 1820 ÷ 1 = 1820.
Step 2: Continue dividing 1820 by numbers until the remainder becomes 0.
1820 ÷ 1 = 1820
1820 ÷ 2 = 910
1820 ÷ 4 = 455
1820 ÷ 5 = 364
1820 ÷ 7 = 260
1820 ÷ 10 = 182
1820 ÷ 13 = 140
1820 ÷ 14 = 130
1820 ÷ 20 = 91
1820 ÷ 26 = 70
1820 ÷ 35 = 52
Therefore, the factors of 1820 are: 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 35, 52, 65, 91, 130, 182, 260, 364, 455, 910, and 1820.
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 1820 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1820 ÷ 2 = 910
910 ÷ 2 = 455
455 ÷ 5 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 1820 are 2, 5, 7, and 13.
The prime factorization of 1820 is: 2² × 5 × 7 × 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, 1820 is divided by 2 to get 910.
Step 2: Now divide 910 by 2 to get 455.
Step 3: Then divide 455 by 5 to get 91.
Step 4: Divide 91 by 7 to get 13.
Here, 13 is a prime number that cannot be divided anymore.
So, the prime factorization of 1820 is: 2² × 5 × 7 × 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 1820: (1, 1820), (2, 910), (4, 455), (5, 364), (7, 260), (10, 182), (13, 140), (14, 130), (20, 91), (26, 70), and (35, 52).
Negative factor pairs of 1820: (-1, -1820), (-2, -910), (-4, -455), (-5, -364), (-7, -260), (-10, -182), (-13, -140), (-14, -130), (-20, -91), (-26, -70), and (-35, -52).
Common Mistakes and How to Avoid Them in Factors of 1820
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 1820, 1 and 1820 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1820 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1820/1.5 ≠ 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 1820 are prime numbers.
For example, 2, 5, 7, and 13 are the prime factors of 1820, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1820 as 2² × 5 × 7 × 13 and missing all the key factors.
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Factors of 1820 Examples
Problem 1
There are 14 people and 1820 sandwiches. How will they divide them equally?
They will get 130 sandwiches each.
Explanation
To divide the sandwiches equally, we need to divide the total sandwiches by the number of people.
1820/14 = 130
Problem 2
A garden is rectangular, the length of the garden is 26 meters and the total area is 1820 square meters. Find the width?
70 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1820 = 26 × width
To find the value of width, we need to shift 26 to the left side.
1820/26 = width
Width = 70.
Problem 3
There are 35 baskets and 1820 apples. How many apples will be in each basket?
Each basket will have 52 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1820/35 = 52
Problem 4
In a conference, there are 1820 attendees, and 130 groups. How many attendees are there in each group?
There are 14 attendees in each group.
Explanation
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1820/130 = 14
Problem 5
1820 books need to be arranged in 140 shelves. How many books will go on each shelf?
Each of the shelves has 13 books.
Explanation
Divide total books by shelves.
1820/140 = 13
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FAQs on Factors of 1820
1.What are the factors of 1820?
2.Mention the prime factors of 1820.
3.Is 1820 a multiple of 13?
4.Mention the factor pairs of 1820?
5.What is the square of 1820?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 1820?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 1820 with numbers?
8.What role do numbers and Factors of 1820 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 1820 skills?
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Important Glossaries for Factor of 1820
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1820 are 1, 2, 4, 5, 7, 10, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, 7, and 13 are prime factors of 1820.
- 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 1820 are (1, 1820), (2, 910), etc.
- Prime factorization: The process of breaking down a number into its basic prime number factors. For 1820, it is 2² × 5 × 7 × 13.
- Multiple: A number that can be divided by another number without a remainder. For example, 1820 is a multiple of 13.
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About BrightChamps in Saudi Arabia
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.
