113 LearnersLast updated on June 10th, 2025
Factors of 1505
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1505, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1505?
The numbers that divide 1505 evenly are known as factors of 1505.
A factor of 1505 is a number that divides the number without a remainder.
The factors of 1505 are 1, 3, 5, 15, 100, 301, and 1505.
Negative factors of 1505: -1, -3, -5, -15, -100, -301, and -1505.
Prime factors of 1505: 3, 5, and 100.
Prime factorization of 1505: 3 × 5 × 100.
The sum of factors of 1505: 1 + 3 + 5 + 15 + 100 + 301 + 1505 = 1930
How to Find Factors of 1505?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1505. Identifying the numbers which are multiplied to get the number 1505 is the multiplication method.
Step 1: Multiply 1505 by 1, 1505 × 1 = 1505.
Step 2: Check for other numbers that give 1505 after multiplying
3 × 501 = 1505
5 × 301 = 1505
15 × 100 = 1505
Therefore, the positive factor pairs of 1505 are: (1, 1505), (3, 501), (5, 301), and (15, 100).
All these factor pairs result in 1505.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1505 by 1, 1505 ÷ 1 = 1505.
Step 2: Continue dividing 1505 by the numbers until the remainder becomes 0.
1505 ÷ 1 = 1505
1505 ÷ 3 = 501
1505 ÷ 5 = 301
1505 ÷ 15 = 100
Therefore, the factors of 1505 are: 1, 3, 5, 15, 100, 301, 1505.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1505 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1505 ÷ 3 = 501
501 ÷ 3 = 167
167 ÷ 5 = 33.4 (not divisible)
167 is a prime number.
The prime factors of 1505 are 3, 5, and 167.
The prime factorization of 1505 is: 3 × 5 × 167.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1505 is divided by 3 to get 501.
Step 2: Now divide 501 by 3 to get 167.
Step 3: 167 is a prime number and cannot be divided further. So, the prime factorization of 1505 is: 3 × 5 × 167.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1505: (1, 1505), (3, 501), (5, 301), and (15, 100).
Negative factor pairs of 1505: (-1, -1505), (-3, -501), (-5, -301), and (-15, -100).
Common Mistakes and How to Avoid Them in Factors of 1505
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1505, 1 and 1505 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1505 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 1505/2.5 = 602, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1505 are prime numbers.
For example, 3 and 5 are the prime factors of 1505, but it has other factors like 15, 100.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1505 as 3 × 5 × 167 and missing all the key factors.
Factors of 1505 Examples
Problem 1
There are 15 employees and 1505 work hours. How will they distribute it evenly?
They will get approximately 100.33 work hours each.
Explanation
To divide the work hours equally, we need to divide the total work hours by the number of employees.
1505/15 ≈ 100.33
Problem 2
A building has a base area of 1505 square meters and a length of 100 meters. Find the width.
15.05 meters.
Explanation
To find the width of the building, we use the formula, Area = length × width
1505 = 100 × width
To find the value of width, we need to shift 100 to the left side.
1505/100 = width
Width = 15.05.
Problem 3
There are 301 students and 1505 books. How many books will each student get?
Each student will get 5 books.
Explanation
To find the books each student gets, divide the total books by the number of students.
1505/301 = 5
Problem 4
In a factory, there are 1505 machines and 5 departments. How many machines are there in each department?
There are 301 machines in each department.
Explanation
Dividing the machines by the total departments, we will get the number of machines in each department.
1505/5 = 301
Problem 5
1505 bricks need to be arranged in 5 rows. How many bricks will go in each row?
Each row will have 301 bricks.
Explanation
Divide total bricks by rows.
1505/5 = 301
FAQs on Factors of 1505
1.What are the factors of 1505?
2.Mention the prime factors of 1505.
3.Is 1505 a multiple of 3?
4.Mention the factor pairs of 1505?
5.What is the square of 1505?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1505?
7.What are some fun ways kids in Qatar can practice Factors of 1505 with numbers?
8.What role do numbers and Factors of 1505 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1505 skills?
Important Glossaries for Factors of 1505
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1505 are 1, 3, 5, 15, 100, 301, and 1505.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 167 are prime factors of 1505.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1505 are (1, 1505), (3, 501), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1505 is 3 × 5 × 167.
- Negative factors: Factors that are negative numbers and divide the original number without leaving a remainder. For example, negative factors of 1505 are -1, -3, -5, etc.
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About BrightChamps in Qatar
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.
