280 LearnersLast updated on May 26th, 2025
Factors of 5400
Factors of 5400 are numbers that can divide 5400 completely without leaving a remainder. We often use factors in organizing events and seating arrangements in our daily lives. In this topic, we will explore the factors of 5400 and the different methods to find them.
What are the Factors of 5400
The factors of 5400 are the numbers that divide 5400 evenly.
The factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 108, 150, 180, 225, 300, 360, 450, 540, 600, 900, 1080, 1350, 1800, and 5400.
Positive factors: These are the positive counterparts of the factors.
Positive factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 108, 150, 180, 225, 300, 360, 450, 540, 600, 900, 1080, 1350, 1800, 5400
Negative factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -108, -150, -180, -225, -300, -360, -450, -540, -600, -900, -1080, -1350, -1800, -5400
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 5400 as the product.
Prime factors: 2, 3, 5
Prime Factorization: Prime factorization involves breaking 5400 into its prime factors.
It is expressed as 2² × 3³ × 5²
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Positive Factors |
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 108, 150, 180, 225, 300, 360, 450, 540, 600, 900, 1080, 1350, 1800, 5400 |
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Negative Factors |
-1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -108, -150, -180, -225, -300, -360, -450, -540, -600, -900, -1080, -1350, -1800, -5400 |
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Prime Factors |
2, 3, 5 |
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Prime Factorization |
2² × 3³ × 5² |
This breakdown helps in understanding the various factors of 5400, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 5400?
There are different methods to find the factors of 5400.
Methods to find the factors of 5400:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 5400 as their product.
Step 1: Find the pair of numbers whose product is 5400.
Step 2: The factors are those numbers, when multiplied, give 5400.
Step 3: Make a list of numbers whose product will be 5400.
A list of numbers whose products are 5400 is given below:
- 1 × 5400 = 5400
- 2 × 2700 = 5400
- 3 × 1800 = 5400
- 4 × 1350 = 5400
- 5 × 1080 = 5400
- 6 × 900 = 5400
- 8 × 675 = 5400
- 9 × 600 = 5400
- 10 × 540 = 5400
- 12 × 450 = 5400
- 15 × 360 = 5400
- 18 × 300 = 5400
- 20 × 270 = 5400
- 25 × 216 = 5400
- 30 × 180 = 5400
- 36 × 150 = 5400
- 45 × 120 = 5400
- 50 × 108 = 5400
- 60 × 90 = 5400
- 75 × 72 = 5400
Thus, the factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 72, 75, 90, 108, 120, 150, 180, 216, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 5400.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 5400 ÷ 1 = 5400
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 72, 75, 90, 108, 120, 150, 180, 216, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 5400.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number and expressed in the form of prime factors, is the prime factorization of a number.
Prime Factors of 5400:
Number 5400 has the following prime factors:
2, 3, 5
To find the prime factors of 5400, we can divide 5400 with the prime numbers like 2, 3, and 5 from the list of factors of 5400.
Step 1: Divide 5400 with the prime number 2
5400 ÷ 2 = 2700
Step 2: Divide 2700 with the prime number 2
2700 ÷ 2 = 1350
Step 3: Divide 1350 with the prime number 2
1350 ÷ 2 = 675
Step 4: Divide 675 with the prime number 3
675 ÷ 3 = 225
Step 5: Divide 225 with the prime number 3
225 ÷ 3 = 75
Step 6: Divide 75 with the prime number 3
75 ÷ 3 = 25
Step 7: Divide 25 with the prime number 5
25 ÷ 5 = 5
Step 8: Divide 5 with the prime number 5
5 ÷ 5 = 1
Prime Factorization of 5400: 2³ × 3³ × 5²
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 5400 into its prime factors: 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5.
In this factor tree, each branch splits into prime factors.
Positive and Negative Factor Pairs of 5400
Factors of 5400 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (25,216), (30,180), (36,150), (45,120), (50,108), (60,90), (72,75)
Negative Factor Pairs: (-1,-5400), (-2,-2700), (-3,-1800), (-4,-1350), (-5,-1080), (-6,-900), (-8,-675), (-9,-600), (-10,-540), (-12,-450), (-15,-360), (-18,-300), (-20,-270), (-25,-216), (-30,-180), (-36,-150), (-45,-120), (-50,-108), (-60,-90), (-72,-75)
Common Mistakes and How to Avoid Them in Factors of 5400
Mistakes can occur while finding the factors. Learn about the common errors that can occur and how to avoid them.
Mistake 1
Confusing prime numbers with factors
Prime numbers are factors of 5400, but not every factor of 5400 is prime. It's essential to distinguish between prime factors and all factors. While 2, 3, and 5 are prime factors, 5400 also has other factors like 1, 4, 6, 9, and 75, which are not prime. Ensure to list all factors, not just the primes.
Solved Examples for Factors of 588.
Problem 1
Can you check whether 75 and 25 are co-prime with respect to the factors of 5400?
No, 75 and 25 are not co-prime with respect to the factors of 5400.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 25: 1, 5, 25
Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 60, 75, 90, 100, 108, 135, 150, 180, 225, 300, 450, 540, 600, 900, 1350, 1800, 5400
Here, the GCF of 75 and 25 is 25, which is greater than 1, so they are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 75 is a multiple of 7 with respect to the factors of 5400.
No, 75 is not a multiple of 7 with respect to the factors of 5400.
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number.
Since 7 is not a factor of 5400, no number can be multiplied by 7 to get 75 as the product.
Problem 3
Identify the perfect square from the factors of 5400.
The perfect square factor of 5400 is 900, and the root is 30.
Explanation
A perfect square is a number we get when the same number is multiplied twice.
When 30 is multiplied twice (30×30), we get the perfect square 900.
So, 900 is a perfect square among the factors of 5400.
Problem 4
Can you check whether 15 and 30 are co-prime with respect to the factors of 5400?
No, 15 and 30 are not co-prime with respect to the factors of 5400.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 15: 1, 3, 5, 15
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 60, 75, 90, 100, 108, 135, 150, 180, 225, 300, 450, 540, 600, 900, 1350, 1800, 5400
Here, the GCF is 15, which is greater than 1, so they are not co-prime.
Problem 5
Verify whether 150 is a factor of 5400.
Yes, 150 is a factor of 5400.
Explanation
A number is a factor of another if it divides the number exactly.
150 divides 5400 without leaving a remainder.
Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 60, 75, 90, 100, 108, 135, 150, 180, 225, 300, 450, 540, 600, 900, 1350, 1800, 5400
Since 150 is listed as a factor, it is indeed a factor of 5400.
FAQs on Factors of 5400
1.What are the factors of 5400?
2.How do you determine if a number is a factor of 5400?
3.What is the smallest factor of 5400?
4.What is the largest factor of 5400?
5.How many factors does 5400 have?
6.How many odd factors does 5400 have?
7.What factors go into 5400?
8.Do any perfect squares exist in the factors of 5400?
9.How can children in Australia use numbers in everyday life to understand Factors of 5400?
10.What are some fun ways kids in Australia can practice Factors of 5400 with numbers?
11.What role do numbers and Factors of 5400 play in helping children in Australia develop problem-solving skills?
12.How can families in Australia create number-rich environments to improve Factors of 5400 skills?
Important glossaries for the Factors of 5400
- Factors: Numbers that divide another number completely without leaving a remainder.
- Prime Factors: Prime numbers that multiply together to give the original number.
- Prime Factorization: The process of breaking down a number into its prime factors.
- Factor Tree: A diagram used to visually represent the prime factorization of a number. It shows the breakdown of a number into its prime factors.
- Co-prime: Two numbers are co-prime if their greatest common divisor (GCD) is 1.
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Hiralee Lalitkumar Makwana
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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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