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786 LearnersLast updated on December 16, 2025
Factors of 45
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 45 easily.
What are the Factors of 45?
Factors of 45 are those numbers that can divide 45 perfectly. The factors of 45 are:
1,3,5,9,15, and 45.
Negative factors of 45: -1, -3, -5, -9, -15, -45
Prime factors of 45: 3,5
Prime factorization of 45: 5×32
The sum of factors of 45: 1+3+5+9+15+45 = 78
The factors of 45 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 45 | 1, 3, 5, 9, 15, 45 |
| Negative Factors of 45 | −1, −3, −5, −9, −15, −45 |
| Prime Factors of 45 | 3, 5 |
| Prime Factorization of 45 | 3 × 3 × 5 = 3² × 5 |
| The Sum of the Factors of 45 | 78 |
How to Find the Factors of 45
For finding factors of 45, we will be learning these below-mentioned methods
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
Finding Factors using Multiplication Methods
This particular method often finds the pair of factors which, on multiplication together, produces 45. Let us find the pairs which, on multiplication, yields 45.
1×45=45
3×15=45
5×9=45
From this, we conclude that, factors of 45 are: 1,3,5,9,15, and 45.
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Finding Factors using Division Method
The division method finds the numbers that evenly divides the given number 45. To find the factors of 45, we have to divide 45 by all possible natural numbers less than 45 and check.
1,3,5,9,15,45 are the only factors that the number 45 has. So to verify the factors of 45 using the division method, we just need to divide 45 by each factor.
45/1 =45
45/3 =15
45/5=9
45/9=5
45/15=3
45/45=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 45 into a product of its prime integers.
Prime Factors of 45
Prime Factors of 45: 3,5.
Prime Factorization of 45
Prime Factorization of : 5×3×3 = 5×32
Factor tree
The number 45 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 45.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 45 are 3 and 15, then proceeding to 15, we get 3 and 5. So, now the factor tree for 45 is achieved.
Factor Pairs of 45
The factors of 45 can be written in both positive and negative pairs. The table below represents the factor pairs of 45, where the product of each pair of numbers is equal to 45.
Positive Pair Factors of 45:
| Factors | Positive Pair Factors |
| 1 × 45 = 45 | 1, 45 |
| 3 × 15 = 45 | 3, 15 |
| 5 × 9 = 45 | 5, 9 |
Since the product of two negative numbers is also positive, 45 also has negative pair factors.
Negative Pair Factors of 45:
| Factors | Negative Pair Factors |
| −1 × −45 = 45 | −1, −45 |
| −3 × −15 = 45 | −3, −15 |
| −5 × −9 = 45 | −5, −9 |
Common Mistakes and How to Avoid Them in Factors of 45
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.
Mistake 2
Leaving the factor 1 and the number itself as the factors in the factor list.
You should know that 1 and the number itself are must-included factors of the given number, other than the remaining factors.
Mistake 3
Not including prime factors like 5 or 3, in the case of 5×9=45 or 3×15=45 and just mention 9 or 15 as factors.
Check all the factors thoroughly, and don’t forget to include prime factors.
Mistake 4
Taking decimal numbers like 2.5 also in the list of factors, where 45 / 2.5=18, leaving a remainder 0.
Decimal numbers can never be factors of any numbers, independent of the fact that some decimal numbers may divide a number evenly.
Mistake 5
Students might use divisibility rules inappropriately and make mistakes like that of including 4 as a factor of 45.
Divisibility rules should be cleared first, then should be applied.
Examples on Factors of 45
Problem 1
Find the GCF of 45 and 60
Factors of 45: 1,3,5,9,15,45
Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60
Common factors of 40 and 60: 1,3,5,15
So, Greatest Common Factor of 40 and 60 is 15.
Answer: 15
Explanation
We first listed out the factors of 40 and 60 and then found the common factors and then identified the greatest common factor from the common list.
Problem 2
Find the LCM of 45 and 75
Prime factorization of 45: 5×32
Prime factorization of 75: 52×3
LCM of 45 and 75: 32×52 = 225.
Answer: 225
Explanation
Did prime factorization of both 45 and 75. The LCM is the product of the highest power of each factor.
How many factors does 45 have?
Problem 3
Find the square root of 45 in the simplest radical form.,A middle school in Dallas is organizing an NFL watch-party fundraiser. The school collects $45 from ticket sales and wants to divide the money equally among student groups buying snacks from Walmart. Which numbers of student groups can divide the $45 evenly with no money left?
Prime factorization of 45: 5×32
√45 = √(5×32) = 3√5
Answer: 3√5
1, 3, 5, 9, 15, 45
Explanation
Finding the square root of 45 by prime factorization method.
To find the possible group counts, we list all the factors of 45. A factor is a number that divides 45 exactly without a remainder. Checking divisibility shows that 1, 3, 5, 9, 15, and 45 divide 45 evenly.
These are all the factors of 45, meaning the money can be split equally among any of these numbers of groups.
Problem 4
A science teacher in Boston buys 45 milligrams of a vitamin supplement from CVS for a lab demonstration. The teacher wants to divide the dosage equally among students so that each student receives the same amount. How many students can receive an equal share with no medicine wasted?
1, 3, 5, 9, 15, 45
Explanation
Equal sharing means the number of students must be a factor of 45.
By listing all numbers that divide 45 exactly, we get 1, 3, 5, 9, 15, and 45. Each of these represents a possible number of students who can receive an equal dosage.
Problem 5
A family drives from Los Angeles (LA) to San Francisco to watch an NBA game. They spend $45 on gas purchased at Costco, and they want to split the cost equally among family members. What are all the possible numbers of people who can split the $45 evenly?
1, 3, 5, 9, 15, 45
Explanation
To split the cost evenly, the number of people must divide 45 with no remainder.
By finding all the factors of 45, we see that 1, 3, 5, 9, 15, and 45 are the only numbers that work. These are all the factors of 45.
FAQs on Factors of 45
1.Is 7 a factor of 45?
2.What are the multiples of 45?
3. Is 45 a factor of 10?
4.Is 12 a factor of 45?
5.Why is 9 a factor of 45?
6.How many factors does 45 have?
7.What is the smallest factor of 45?
8.What is the largest factor of 45?
9.Which factors of 45 add up to 13?
10.How many even factors does 45 have?
11.What are the odd factors of 45?
12.What is the sum of all the factors of 45?
Important Terms Related to Factors of 45
- 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.
