102 LearnersLast updated on May 26th, 2025
Factors of 507
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 507, how they are used in real life, and tips to learn them quickly.
What are the Factors of 507?
The numbers that divide 507 evenly are known as factors of 507. A factor of 507 is a number that divides the number without a remainder. The factors of 507 are 1, 3, 13, 39, 169, and 507. Negative factors of 507: -1, -3, -13, -39, -169, and -507. Prime factors of 507: 3 and 13. Prime factorization of 507: 3 × 13 × 13. The sum of factors of 507: 1 + 3 + 13 + 39 + 169 + 507 = 732
How to Find Factors of 507?
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 507. Identifying the numbers that are multiplied to get the number 507 is the multiplication method. Step 1: Multiply 507 by 1, 507 × 1 = 507. Step 2: Check for other numbers that give 507 after multiplying 3 × 169 = 507 13 × 39 = 507 Therefore, the positive factor pairs of 507 are: (1, 507), (3, 169), (13, 39). All these factor pairs result in 507. 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 507 by 1, 507 ÷ 1 = 507. Step 2: Continue dividing 507 by the numbers until the remainder becomes 0. 507 ÷ 1 = 507 507 ÷ 3 = 169 507 ÷ 13 = 39 Therefore, the factors of 507 are: 1, 3, 13, 39, 169, 507.
Prime Factors and Prime Factorization
The factors can be found by dividing it with 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 507 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 507 ÷ 3 = 169 169 ÷ 13 = 13 13 ÷ 13 = 1 The prime factors of 507 are 3 and 13. The prime factorization of 507 is: 3 × 13 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows - Step 1: Firstly, 507 is divided by 3 to get 169. Step 2: Now divide 169 by 13 to get 13. Step 3: 13 is a prime number and cannot be divided further. So, the prime factorization of 507 is: 3 × 13 × 13. 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 507: (1, 507), (3, 169), (13, 39). Negative factor pairs of 507: (-1, -507), (-3, -169), (-13, -39).
Common Mistakes and How to Avoid Them in Factors of 507
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 word. Always remember to include 1 and the number itself. For example, in factors of 507, 1 and 507 are also factors.
Factors of 507 Examples
Problem 1
There are 3 teams and 507 marbles. How will they divide it equally?
They will get 169 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of teams. 507/3 = 169
Problem 2
A garden is rectangular, the length of the garden is 13 meters and the total area is 507 square meters. Find the width?
39 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 507 = 13 × width To find the value of width, we need to shift 13 to the left side. 507/13 = width Width = 39.
Problem 3
There are 169 gift boxes and 507 candies. How many candies will be in each box?
Each box will have 3 candies.
Explanation
To find the candies in each box, divide the total candies with the boxes. 507/169 = 3
Problem 4
In a library, there are 507 books, and 13 shelves. How many books are there on each shelf?
There are 39 books on each shelf.
Explanation
Dividing the books with the total shelves, we will get the number of books on each shelf. 507/13 = 39
Problem 5
507 apples need to be packed in 13 crates. How many apples will go in each crate?
Each of the crates has 39 apples.
Explanation
Divide total apples with crates. 507/13 = 39
FAQs on Factors of 507
1.What are the factors of 507?
2.Mention the prime factors of 507.
3.Is 507 a multiple of 3?
4.Mention the factor pairs of 507?
5.What is the square of 507?
Important Glossaries for Factor of 507
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 507 are 1, 3, 13, 39, 169, and 507. Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 507. 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 507 are (1, 507), (3, 169), and (13, 39). Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to the given number. Division method: A process to find factors by dividing the given number by whole numbers and checking for zero remainders.
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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.
