418 LearnersLast updated on May 26th, 2025
Factors of 54
Factors of any number are the whole numbers that can divide the number completely. Why are factors important to learn? For mathematical approaches, factors are used in organizing and bringing more efficiency to any task. In this article, let's learn how to solve factors of 54 easily.
What are the Factors of 54?
Factors of 54 are those numbers that can divide 54 perfectly. The factors of 54 are:
1,2,3,6,9,18,27, and 54.
Negative factors of 54: -1, -2, -3 -6, -9, -18, -27, -54
Prime factors of 54: 2,3
Prime factorization of 54: 33×2
The sum of factors of 54: 1+2+3+6+9+18+27+54= 120
How to Find the Factors of 54
For finding factors of 54, we will be learning these below-mentioned methods:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors using Multiplication Methods
This particular method often finds the pair of factors which, on multiplication together, produces 54. Let us find the pairs which, on multiplication, yields 54.
1×54=54
2×27=54
3×18=54
6×9=54
From this, we conclude that, factors of 54 are:1,2,3,6,9,18,27, and 54.
Finding Factors using Division Method
The division method finds the numbers that evenly divides the given number 54. To find the factors of 54, we have to divide 54 by all possible natural numbers less than 54 and check.
1,2,3,6,9,18,27, 54 are the only factors that the number 54 has. So to verify the factors of 54 using the division method, we just need to divide 54 by each factor.
54/1 =54
54/2 =27
54/3=18
54/6=9
54/9=6
54/18=3
54/27=2
54/54=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 54 into a product of its prime integers.
Prime Factors of 54: 2,3.
Prime Factorization of 54: 3×3×3×2 = 33×2
Factor tree
The number 54 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 54.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 54 are 2 and 27, then proceeding to 27, we get 3 and 9. Similarly, for 9: 3 and 3
Factor Pairs:
Positive pair factors: (1,54), (2,27), (3,18), (6,9)
Negative pair factors: (-1,-54), (-2,-27), (-3,-18), (-6,-9).
Common Mistakes and How to Avoid Them in Factors of 54
Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them.
Mistake 1
Misconception and confusion about factors with that of multiples.
Factors are way different from multiples. You need to understand it clearly that factors are integers which divide a given number evenly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 54 Examples
Problem 1
Find the GCF of 54 and 72
Factors of 54: 1,2,3,6,9,18,27, 54
Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72
Common factors of 54 and 72: 1,2,3,6,9,18
So, the Greatest Common Factor of 54 and 72 is 18.
Answer: 18
Explanation
We first listed out the factors of 54 and 72 and then found the common factors and then identified the greatest common factor from the common list.
Problem 2
Find the LCM of 54 and 72
Prime factorization of 54: 2×33.
Prime factorization of 72: 23×32
LCM of 54 and 72: 33×23 = 216.
Answer: 216
Explanation
Did prime factorization of both 72 and 54. The LCM is the product of the highest power of each factor.
Problem 3
The area of a rectangle is 54 square units. If the length is 9 units, then what is the measure of its width?
Area of rectangle: 54 sq units
Factors of 54: 1,2,3,6,9,18,27, 54
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 9 units
There exists a factor pair of 54, which is (6,9). Hence, width is 6 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 9 × width = 54
⇒ width = 54/9 = 6
Answer: 6 units
Explanation
Used the concept of factor pairs for 54 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 2,6,18 and 27.
Prime factorization of 2: 2×1.
Prime factorization of 6: 3×2
Prime factorization of 18: 32×2
Prime factorization of 27: 33
LCM of 2,6,18 and 27: 2×33 = 54
Answer: 54 is the smallest number which is divisible by 2,6,18,27.
Explanation
To find the smallest number which is divisible by 2,6,18,27, we need to find the LCM of these numbers.
Problem 5
What is the sum of the factors of 54 and 55?
Factors of 54: 1,2,3,6,9,18,27, 54
Sum of the factors: 1+2+3+6+9+18+27+54= 120
Factors of 55: 1,5,11,55
Sum of the factors: 1+5+11+55 =72
Explanation
added all factors togather to find the sum.
FAQs on Factors of 54
1.What is 54 divisible by?
2.How to find factors of a number?
3.Is 54 a factor of 12?
4.Is 6 a factor of 54?
5.Does 54 go into 3?
6.How can children in Canada use numbers in everyday life to understand Factors of 54?
7.What are some fun ways kids in Canada can practice Factors of 54 with numbers?
8.What role do numbers and Factors of 54 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 54 skills?
Important Glossaries for Factors of 54
- Ratio - Ratio of two numbers compares between them, how many times one number contains the other number. It is expressed as m:n, where m and n are two positive numbers whose ratio is to be shown.
- Factors - These are numbers that divide the given number without leaving any remainder or the remainder as 0.
- Prime Factorization - It involves factoring the number into its prime factors.
- Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
- Composite numbers - These are numbers having more than two factors.
- Multiple - It is a product of the given number and any other integer.
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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.
