117 LearnersLast updated on May 26th, 2025
Factors of 36000
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 36000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 36000?
The numbers that divide 36000 evenly are known as factors of 36000.
A factor of 36000 is a number that divides the number without remainder.
The factors of 36000 are numerous, including 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 900, 1200, 1800, 2400, 3600, 7200, 12000, 18000, and 36000.
Negative factors of 36000: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -30, -36, -40, -45, -48, -50, -60, -72, -75, -80, -90, -100, -120, -144, -150, -180, -200, -225, -240, -288, -300, -360, -400, -450, -480, -600, -720, -900, -1200, -1800, -2400, -3600, -7200, -12000, -18000, and -36000.
Prime factors of 36000: 2, 3, and 5.
Prime factorization of 36000: 25 × 32 × 53.
The sum of factors of 36000: This is a complex calculation due to the high number of factors, but it can be computed using the formula for the sum of divisors.
How to Find Factors of 36000?
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 the pairs of numbers that are multiplied to give 36000. Identifying the numbers which are multiplied to get the number 36000 is the multiplication method.
Step 1: Multiply 36000 by 1, 36000 × 1 = 36000.
Step 2: Check for other numbers that give 36000 after multiplying:
2 × 18000 = 36000
3 × 12000 = 36000
4 × 9000 = 36000
5 × 7200 = 36000
6 × 6000 = 36000
8 × 4500 = 36000
9 × 4000 = 36000
10 × 3600 = 36000 ... and so on.
Therefore, the positive factor pairs of 36000 are extensive. 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 in whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 36000 by 1, 36000 ÷ 1 = 36000.
Step 2: Continue dividing 36000 by the numbers until the remainder becomes 0.
36000 ÷ 1 = 36000
36000 ÷ 2 = 18000
36000 ÷ 3 = 12000
36000 ÷ 4 = 9000
36000 ÷ 5 = 7200
36000 ÷ 6 = 6000 ... and so on.
Therefore, the factors of 36000 include 1, 2, 3, 4, 5, 6, and many more.
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 36000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
36000 ÷ 2 = 18000
18000 ÷ 2 = 9000
9000 ÷ 2 = 4500
4500 ÷ 2 = 2250
2250 ÷ 2 = 1125
1125 ÷ 3 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 36000 are 2, 3, and 5.
The prime factorization of 36000 is: 25 × 32 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 36000 is divided by 2 to get 18000.
Step 2: Now divide 18000 by 2 to get 9000.
Step 3: Then divide 9000 by 2 to get 4500.
Step 4: Divide 4500 by 2 to get 2250.
Step 5: Continue dividing by 2 to get 1125.
Step 6: Divide by 3 to get 375.
Step 7: Divide by 3 to get 125.
Step 8: Finally, divide by 5 to get 25 and then 5 again to get 1. So, the prime factorization of 36000 is: 25 × 32 × 53.
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 36000: (1, 36000), (2, 18000), (3, 12000), (4, 9000), (5, 7200), (6, 6000), (8, 4500), (9, 4000), (10, 3600), ... and so on.
Negative factor pairs of 36000: (-1, -36000), (-2, -18000), (-3, -12000), (-4, -9000), (-5, -7200), (-6, -6000), (-8, -4500), (-9, -4000), (-10, -3600), ... and so on.
Common Mistakes and How to Avoid Them in Factors of 36000
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 36000, 1 and 36000 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 36000 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 36000/1.5 = 24000, and it is not 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 36000 are prime numbers. While 2, 3, and 5 are the prime factors of 36000, it has other factors like 4, 6, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 36000 as 25 × 32 × 53 and missing key factors.
Factors of 36000 Examples
Problem 1
A gardener has 36000 seeds and wants to plant them in equal rows with 60 seeds in each row. How many rows will the gardener have?
The gardener will have 600 rows.
Explanation
To find the number of rows, divide the total seeds by the number of seeds per row.
36000/60 = 600
Problem 2
A rectangular courtyard has a length of 180 meters and an area of 36000 square meters. Find the width.
200 meters.
Explanation
To find the width of the field, use the formula:
Area = length × width
36000 = 180 × width
To find the value of width, divide 36000 by 180.
36000/180 = width
Width = 200
Problem 3
A company has 36000 brochures to be packed into 300 boxes equally. How many brochures will each box contain?
Each box will contain 120 brochures.
Explanation
To find the number of brochures in each box, divide the total brochures by the number of boxes.
36000/300 = 120
Problem 4
An auditorium has 36000 seats and is divided into sections with 400 seats each. How many sections are there?
There are 90 sections.
Explanation
Dividing the total seats by the number of seats per section gives the number of sections.
36000/400 = 90
Problem 5
A factory produces 36000 gadgets in a month and packages them into 600 crates. How many gadgets are there in each crate?
Each crate contains 60 gadgets.
Explanation
Divide the total number of gadgets by the number of crates to find the number of gadgets per crate. 36000/600 = 60
FAQs on Factors of 36000
1.What are the factors of 36000?
2.Mention the prime factors of 36000.
3.Is 36000 a multiple of 9?
4.Mention the factor pairs of 36000.
5.What is the square of 36000?
Important Glossaries for Factors of 36000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 36000 include 1, 2, 3, 4, 5, 6, and many more.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 36000.
- 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 36000 are (1, 36000), (2, 18000), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 36000.
- Division method: A technique used to find factors by dividing the given number by whole numbers and finding those that result in a remainder of 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.
Fun Fact
: She loves to read number jokes and games.
