101 LearnersLast updated on May 26th, 2025
Factors of -504
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 -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 remainder.
The factors of -504 include both positive and negative numbers: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -56, -63, -72, -84, -126, -168, -252, -504, 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 of -504: 2, 3, and 7.
Prime factorization of -504: -1 × 2³ × 3² × 7.
The sum of the positive 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 = 1560
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 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), and (21, -24).
For every positive factor, there is a corresponding negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following the 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 include both positive and negative factors: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -56, -63, -72, -84, -126, -168, -252, -504, 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 and Prime Factorization
The factors can be found by dividing 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: -1 × 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: -1 × 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), and (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), and (-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.
Factors of -504 Examples
Problem 1
There are 504 seats in a theater, arranged in 7 rows. How many seats are there in each row?
There are 72 seats in each row.
Explanation
To find the seats in each row, divide the total seats by the number of rows.
504/7 = 72
Problem 2
A construction project requires -504 bricks, and each bundle contains 42 bricks. How many bundles are needed?
12 bundles.
Explanation
To find the number of bundles needed, divide the total number of bricks by the number of bricks in each bundle. -504/42 = -12 (negative sign indicates direction or assumption)
Problem 3
A school has 504 students and wants to divide them into groups of 9. How many groups can be formed?
56 groups can be formed.
Explanation
To find the number of groups, divide the total number of students by the number of students per group.
504/9 = 56
Problem 4
A factory produces 504 products in 6 days. How many products are produced per day?
84 products are produced per day.
Explanation
Dividing the total products by the number of days, we find the daily production rate.
504/6 = 84
Problem 5
In a storage unit, 504 items are to be packed into boxes of 12. How many boxes are required?
42 boxes are required.
Explanation
Divide the total items by the number of items per box to find the number of boxes needed.
504/12 = 42
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 6?
4.Mention the factor pairs of -504.
5.What is the absolute value of -504?
Important Glossaries for Factors of -504
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -504 include -1, -2, -3, etc.
- 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, factor pairs of -504 include (-1, 504), (2, -252), etc.
- Negative factors: These are factors that are negative integers. For example, -1, -2, -3 are negative factors of -504.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of -504 is -1 × 2³ × 3² × 7.
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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.
