113 LearnersLast updated on June 10th, 2025
Factors of 1506
Factors are the numbers that divide any given number evenly without 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 1506, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1506?
The numbers that divide 1506 evenly are known as factors of 1506.
A factor of 1506 is a number that divides the number without remainder.
The factors of 1506 are 1, 2, 3, 6, 251, 502, 753, and 1506.
Negative factors of 1506: -1, -2, -3, -6, -251, -502, -753, and -1506.
Prime factors of 1506: 2, 3, and 251.
Prime factorization of 1506: 2 × 3 × 251.
The sum of factors of 1506: 1 + 2 + 3 + 6 + 251 + 502 + 753 + 1506 = 3024
How to Find Factors of 1506?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 1506. Identifying the numbers which are multiplied to get the number 1506 is the multiplication method.
Step 1: Multiply 1506 by 1, 1506 × 1 = 1506.
Step 2: Check for other numbers that give 1506 after multiplying
2 × 753 = 1506
3 × 502 = 1506
6 × 251 = 1506
Therefore, the positive factor pairs of 1506 are: (1, 1506), (2, 753), (3, 502), (6, 251).
All these factor pairs result in 1506.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 1506 by 1, 1506 ÷ 1 = 1506.
Step 2: Continue dividing 1506 by the numbers until the remainder becomes 0.
1506 ÷ 1 = 1506
1506 ÷ 2 = 753
1506 ÷ 3 = 502
1506 ÷ 6 = 251
Therefore, the factors of 1506 are: 1, 2, 3, 6, 251, 502, 753, 1506.
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 1506 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1506 ÷ 2 = 753
753 ÷ 3 = 251
251 ÷ 251 = 1
The prime factors of 1506 are 2, 3, and 251.
The prime factorization of 1506 is: 2 × 3 × 251.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1506 is divided by 2 to get 753.
Step 2: Now divide 753 by 3 to get 251.
Step 3: Then divide 251 by 251 to get 1. Here, 251 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1506 is: 2 × 3 × 251.
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 1506: (1, 1506), (2, 753), (3, 502), (6, 251).
Negative factor pairs of 1506: (-1, -1506), (-2, -753), (-3, -502), (-6, -251).
Common Mistakes and How to Avoid Them in Factors of 1506
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 1506, 1 and 1506 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 1506 consist of -1, -2, -3, 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 1.5 as a factor, because 1506/1.5 = 1004, 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 1506 are prime numbers.
For example, 2, 3, and 251 are the prime factors of 1506, but it has other factors like 6, 502.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1506 as 2 × 3 × 251 and missing all the key factors.
Factors of 1506 Examples
Problem 1
There are 6 teams and 1506 participants. How will they divide equally among the teams?
Each team will have 251 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1506/6 = 251
Problem 2
A rectangular garden has a length of 502 meters and a total area of 1506 square meters. Find the width.
3 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1506 = 502 × width
To find the value of width, we need to divide 1506 by 502.
1506/502 = width
Width = 3.
Problem 3
There are 3 delivery trucks and 1506 packages. How many packages will each truck carry?
Each truck will carry 502 packages.
Explanation
To find the packages each truck will carry, divide the total packages by the number of trucks.
1506/3 = 502
Problem 4
In a concert, there are 1506 attendees and 2 entrance gates. How many attendees enter through each gate?
753 attendees enter through each gate.
Explanation
Dividing the attendees by the number of entrance gates will give the number of attendees per gate.
1506/2 = 753
Problem 5
A publisher needs to distribute 1506 books into 3 warehouses. How many books will each warehouse receive?
Each warehouse will receive 502 books.
Explanation
Divide the total number of books by the number of warehouses.
1506/3 = 502
FAQs on Factors of 1506
1.What are the factors of 1506?
2.Mention the prime factors of 1506.
3.Is 1506 a multiple of 3?
4.Mention the factor pairs of 1506.
5.What is the square of 1506?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1506?
7.What are some fun ways kids in Qatar can practice Factors of 1506 with numbers?
8.What role do numbers and Factors of 1506 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1506 skills?
Important Glossaries for Factor of 1506
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1506 are 1, 2, 3, 6, 251, 502, 753, and 1506.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 251 are prime factors of 1506.
- 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 1506 are (1, 1506), (2, 753), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
- Division method: A method to find factors by dividing the original number by whole numbers until the remainder is zero.
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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.
