124 LearnersLast updated on May 26th, 2025
Factors of 504
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 504, how they are used in real life, and tips to learn them quickly.
What are the Factors of 504?
The numbers that divide 504 evenly are known as factors of 504. A factor of 504 is a number that divides the number without a remainder. The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504. Negative factors of 504: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -56, -63, -72, -84, -126, -168, -252, -504. Prime factors of 504: 2, 3, and 7. Prime factorization of 504: 2³ × 3² × 7. The sum of factors of 504: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 28 + 36 + 42 + 56 + 63 + 72 + 84 + 126 + 168 + 252 + 504 = 1440
How to Find Factors of 504?
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 504. Identifying the numbers which are multiplied to get the number 504 is the multiplication method. Step 1: Multiply 504 by 1, 504 × 1 = 504. Step 2: Check for other numbers that give 504 after multiplying 2 × 252 = 504 3 × 168 = 504 4 × 126 = 504 6 × 84 = 504 7 × 72 = 504 8 × 63 = 504 9 × 56 = 504 12 × 42 = 504 14 × 36 = 504 18 × 28 = 504 21 × 24 = 504 Therefore, the positive factor pairs of 504 are: (1, 504), (2, 252), (3, 168), (4, 126), (6, 84), (7, 72), (8, 63), (9, 56), (12, 42), (14, 36), (18, 28), (21, 24). All these factor pairs result in 504. 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 in whole numbers as factors. Factors can be calculated by following a simple division method - Step 1: Divide 504 by 1, 504 ÷ 1 = 504. Step 2: Continue dividing 504 by the numbers until the remainder becomes 0. 504 ÷ 1 = 504 504 ÷ 2 = 252 504 ÷ 3 = 168 504 ÷ 4 = 126 504 ÷ 6 = 84 504 ÷ 7 = 72 504 ÷ 8 = 63 504 ÷ 9 = 56 504 ÷ 12 = 42 504 ÷ 14 = 36 504 ÷ 18 = 28 504 ÷ 21 = 24 Therefore, the factors of 504 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 504 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 504 ÷ 2 = 252 252 ÷ 2 = 126 126 ÷ 2 = 63 63 ÷ 3 = 21 21 ÷ 3 = 7 7 ÷ 7 = 1 The prime factors of 504 are 2, 3, and 7. The prime factorization of 504 is: 2³ × 3² × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows - Step 1: Firstly, 504 is divided by 2 to get 252. Step 2: Now divide 252 by 2 to get 126. Step 3: Then divide 126 by 2 to get 63. Step 4: Divide 63 by 3 to get 21. Step 5: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 504 is: 2³ × 3² × 7. 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 504: (1, 504), (2, 252), (3, 168), (4, 126), (6, 84), (7, 72), (8, 63), (9, 56), (12, 42), (14, 36), (18, 28), (21, 24). Negative factor pairs of 504: (-1, -504), (-2, -252), (-3, -168), (-4, -126), (-6, -84), (-7, -72), (-8, -63), (-9, -56), (-12, -42), (-14, -36), (-18, -28), (-21, -24).
Common Mistakes and How to Avoid Them in Factors of 504
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 504, 1 and 504 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 504 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 504/1.5 = 336, 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 504 are prime numbers. For example, 2, 3, and 7 are the prime factors of 504, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 504 as 2³ × 3² × 7 and missing all the key factors.
Factors of 504 Examples
Problem 1
There are 504 apples and 12 baskets. How will they divide it equally?
They will get 42 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets. 504/12 = 42
Problem 2
A garden is rectangular, the length of the garden is 36 meters and the total area is 504 square meters. Find the width?
14 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 504 = 36 × width To find the value of width, we need to shift 36 to the left side. 504/36 = width Width = 14.
Problem 3
There are 42 teams and 504 players. How many players will be in each team?
Each team will have 12 players.
Explanation
To find the players in each team, divide the total players by the number of teams. 504/42 = 12
Problem 4
In a conference, there are 504 people, and 7 groups. How many people are there in each group?
There are 72 people in each group.
Explanation
Dividing the people by the total groups, we will get the number of people in each group. 504/7 = 72
Problem 5
504 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 84 books.
Explanation
Divide total books by shelves. 504/6 = 84
FAQs on Factors of 504
1.What are the factors of 504?
2.Mention the prime factors of 504.
3.Is 504 a multiple of 9?
4.Mention the factor pairs of 504?
5.What is the square of 504?
6.How can children in Australia use numbers in everyday life to understand Factors of 504?
7.What are some fun ways kids in Australia can practice Factors of 504 with numbers?
8.What role do numbers and Factors of 504 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 504 skills?
Important Glossaries for Factor of 504
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504. Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 504. 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 504 are (1, 504), (2, 252), etc. Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 504 is 2³ × 3² × 7. Division method: A method to find factors by dividing the number by integers until the remainder is zero. For example, finding factors of 504 using division.
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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
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