339 LearnersLast updated on May 26th, 2025
Factors of 165
Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 165. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 165.
What are the Factors of 165?
The factors of 165 or the numbers which divide 165 exactly are:
1,3,5,11,15,33,55, and 165.
Negative factors of 165: -1,-3,-5,-11,-15,-33,-55,-165.
Prime factors of 165: 3,5,11
Prime factorization of 165: 3×5×11
The sum of factors of 165: 1+3+5+11+15+33+55+165= 288
How to Find the Factors of 165
For finding factors of 165, 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 165. Let us find the pairs which, on multiplication, yields 165.
1×165=165
3×55=165
5×33=165
11×15=165
So, factors of 165 are: 1,3,5,11,15,33,55, and 165.
Finding Factors using Division Method
The division method finds the factors that evenly divides the given number 165. In this process, we have to divide 165 by all possible natural numbers less than 165 and check.
1,3,5,11,15,33,55, and 165 are the only factors that the number 165 has. So to verify the factors of 165 using the division method, we just need to divide 165 by each factor.
165/1 =165
165/3=55
165/5=33
165/11=15
165/15=11
165/33=5
165/55=3
165/165=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 165 into a product of its prime integers.
Prime Factors of 165: 3,5,11.
Prime Factorization of 165: 3×5×15
Factor tree
The number 165 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 165.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 165 are 3 and 55, then proceeding to 55, we get 5 and 11. So, now the factor tree for 165 is achieved.
Factor Pairs
Positive pair factors: (1,165), (3,55), (5,33), (11,15).
Negative pair factors: (-1,-154), (-3,-55), (-5,-33), (-11,-15).
Common Mistakes and How to Avoid Them in Factors of 165
Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them.
Mistake 1
Factors might be larger than the given number.
Factors can never be larger than the given number, but multiples can be. You need to understand the concept that factors are integers which divide a given number perfectly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 165 Examples
Problem 1
A lady has 165 dahlias and 55 roses. She wants to divide them equally among some vases. What is the maximum number of vases she requires?
Number of dahlias: 165
Number of roses: 55
Factors of 165: 1,3,5,11,15,33,55,165
Factors of 55: 1,5,11,55
Common factors of 165 and 55: 1,5,11,55.
Greatest common factor of 165 and 55: 55
So, there will be 55 vases she requires.
Answer: 55 vases
Explanation
To divide equally, the maximum number of plates can be found through the Greatest Common Factor. Here, we found the GCF, which is the answer.
Problem 2
Find the simplest form of square root of 165.
√165 = √(3×5×11) = √165
Answer: The simplest form of square root of 165 is √165.
Explanation
Break down 165 into its product of its prime factor and find its square root by grouping a pair of factors at a time, leaving the remaining single factors under radical.
Problem 3
The area of a rectangle is 165 square units. If the length is 33 units, then what is the measure of its width?
Area of rectangle: 165 sq units
Factors of 165: 1,3,5,11,15,33,55,165
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 33 units
There exists a factor pair of 165, which is (5,33). Hence, width is 5 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 33 × width = 165
⇒ width = 165/33 = 5
Answer: 5 units
Explanation
Used the concept of factor pairs for 165 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 5 and 33.
Prime factorization of 5: 5×1.
Prime factorization of 33: 3×11
LCM of 5 and 33: 3×5×11 = 165
Answer: 165 is the smallest number which is divisible by 5 and 33
Explanation
To find the smallest number which is divisible by 5 and 33, we need to find the LCM of these numbers.
Problem 5
If a number is divisible by both 3 and 55, is it divisible by 165?
Yes, any number which is divisible by 3 and 55 is also divisible by 165, since 165 = 3×55
Answer: Yes
Explanation
Any number which is divisible by the factor 3 and factor 55 of 165, then it is also divisible by 165 because 165 is a product of 3 and 55.
FAQs on Factors of 165
1.What is 165 divided by prime numbers?
2.Is 11 a factor of 165?
3.Can 165 be divided by 3?
4.Is 165 divisible by 6?
5.Is 165 divisible by 4?
6.How can children in India use numbers in everyday life to understand Factors of 165?
7.What are some fun ways kids in India can practice Factors of 165 with numbers?
8.What role do numbers and Factors of 165 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 165 skills?
Important Glossaries for Factors of 165
- Multipliers - Number which multiplies or a number by which another number is multiplied.
- Dividers - A number that divides.
- 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 India
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.
