302 LearnersLast updated on May 26th, 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
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
- Factor Tree
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.
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: 3,5.
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:
Positive pair factors: (1,45), (3,15), and (5,9)
Negative pair factors: (-1,-45), (-3,-15), and (-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.
Factors of 45 Examples
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
How many factors does 45 have?
Factors of 45: 1,3,5,9,15,45
So. 45 has 6 factors.
Answer: 6
Explanation
List out all the factors of 45 and count them.
Problem 4
Find the square root of 45 in the simplest radical form.
Prime factorization of 45: 5×32
√45 = √(5×32) = 3√5
Answer: 3√5
Explanation
Finding the square root of 45 by prime factorization method.
Problem 5
If a number is divisible by both 3 and 15, is it divisible by 45?
Yes, any number which is divisible by 3 and 15 is also divisible by 45, since 45 = 3×15
Answer: Yes
Explanation
Any number which is divisible by the factor 3 and factor 15 of 45, then it is also divisible by 45 because 45 is a product of 15 and 3.
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 can children in Thailand use numbers in everyday life to understand Factors of 45?
7.What are some fun ways kids in Thailand can practice Factors of 45 with numbers?
8.What role do numbers and Factors of 45 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 45 skills?
Important Glossaries for 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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About BrightChamps in Thailand
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.
