100 LearnersLast updated on May 26th, 2025
Factors of 61800
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 61800, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 61800?
The numbers that divide 61800 evenly are known as factors of 61800.
A factor of 61800 is a number that divides the number without remainder.
The factors of 61800 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 31, 60, 62, 93, 124, 155, 186, 310, 372, 465, 620, 930, 1860, 2015, 3720, 4030, 6050, 8060, 12075, 16120, 24150, 48300, and 61800.
Negative factors of 61800: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, -31, -60, -62, -93, -124, -155, -186, -310, -372, -465, -620, -930, -1860, -2015, -3720, -4030, -6050, -8060, -12075, -16120, -24150, -48300, and -61800.
Prime factors of 61800: 2, 3, 5, and 31.
Prime factorization of 61800: (23 times 3 times 52 times 31).
The sum of factors of 61800: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 31 + 60 + 62 + 93 + 124 + 155 + 186 + 310 + 372 + 465 + 620 + 930 + 1860 + 2015 + 3720 + 4030 + 6050 + 8060 + 12075 + 16120 + 24150 + 48300 + 61800 = 188760.
How to Find Factors of 61800?
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 61800. Identifying the numbers which are multiplied to get the number 61800 is the multiplication method.
Step 1: Multiply 61800 by 1, 61800 × 1 = 61800.
Step 2: Check for other numbers that give 61800 after multiplying:
(2 times 30900 = 61800)
(3 times 20600 = 61800)
(4 times 15450 = 61800)
(5 times 12360 = 61800)
(6 times 10300 = 61800)
(10 times 6180 = 61800)
Therefore, the positive factor pairs of 61800 include: (1, 61800), (2, 30900), (3, 20600), (4, 15450), (5, 12360), (6, 10300), (10, 6180), etc. 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 the simple division method -
Step 1: Divide 61800 by 1, 61800 ÷ 1 = 61800.
Step 2: Continue dividing 61800 by the numbers until the remainder becomes 0:
(61800 ÷ 1 = 61800)
(61800 ÷ 2 = 30900)
(61800 ÷ 3 = 20600)
(61800 ÷ 4 = 15450)
(61800 ÷ 5 = 12360)
(61800 ÷ 6 = 10300)
Therefore, the factors of 61800 include: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 31, 60, 62, 93, 124, 155, 186, 310, 372, 465, 620, 930, 1860, 2015, 3720, 4030, 6050, 8060, 12075, 16120, 24150, 48300, and 61800.
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 61800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
(61800 ÷ 2 = 30900)
(30900 ÷ 2 = 15450)
(15450 ÷ 2 = 7725)
(7725 ÷ 3 = 2575)
(2575 ÷ 5 = 515)
(515 ÷ 5 = 103)
(103 ÷ 31 = 1)
The prime factors of 61800 are 2, 3, 5, and 31.
The prime factorization of 61800 is: (23 times 3 times 52 times 31).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 61800 is divided by 2 to get 30900.
Step 2: Now divide 30900 by 2 to get 15450.
Step 3: Then divide 15450 by 2 to get 7725.
Step 4: Divide 7725 by 3 to get 2575.
Step 5: Divide 2575 by 5 to get 515.
Step 6: Divide 515 by 5 to get 103.
Step 7: Finally, divide 103 by 31 to get 1. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 61800 is: (23 times 3 times 52 times 31).
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 61800: (1, 61800), (2, 30900), (3, 20600), (4, 15450), (5, 12360), (6, 10300), (10, 6180), etc.
Negative factor pairs of 61800: (-1, -61800), (-2, -30900), (-3, -20600), (-4, -15450), (-5, -12360), (-6, -10300), (-10, -6180), etc.
Common Mistakes and How to Avoid Them in Factors of 61800
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 61800, 1 and 61800 are also factors.
Factors of 61800 Examples
Problem 1
There are 10 teams and 61800 tickets. How will they distribute it equally?
They will get 6180 tickets each.
Explanation
To divide the tickets equally, we need to divide the total tickets with the number of teams.
61800/10 = 6180
Problem 2
A rectangular garden has a length of 62 meters and the total area is 61800 square meters. Find the width?
997 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
61800 = 62 × width
To find the value of width, we need to shift 62 to the left side.
61800/62 = width
Width = 997.
Problem 3
There are 15 sections and 61800 books. How many books will be in each section?
Each section will have 4120 books.
Explanation
To find the books in each section, divide the total books with the sections.
61800/15 = 4120
Problem 4
In a warehouse, there are 61800 boxes and 60 shelves. How many boxes are there on each shelf?
There are 1030 boxes on each shelf.
Explanation
Dividing the boxes with the total shelves, we will get the number of boxes on each shelf.
61800/60 = 1030
Problem 5
61800 flowers need to be arranged in 31 vases. How many flowers will go in each vase?
Each vase will have 1994 flowers.
Explanation
Divide the total flowers with the vases.
61800/31 = 1994
FAQs on Factors of 61800
1.What are the factors of 61800?
2.Mention the prime factors of 61800.
3.Is 61800 a multiple of 31?
4.Mention the factor pairs of 61800?
5.What is the square of 61800?
6.How can children in Singapore use numbers in everyday life to understand Factors of 61800?
7.What are some fun ways kids in Singapore can practice Factors of 61800 with numbers?
8.What role do numbers and Factors of 61800 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of 61800 skills?
Important Glossaries for Factor of 61800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 61800 include 1, 2, 3, 4, 5, 6, 10, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 31 are prime factors of 61800.
- 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 61800 include (1, 61800), (2, 30900), (3, 20600), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 61800 is (23 times 3 times 52 times 31).
- Multiple: A number is a multiple of another number if it can be divided by that number without a remainder. For example, 61800 is a multiple of 31.
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About BrightChamps in Singapore
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.
