Last updated on May 26th, 2025
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.
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
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
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.
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.
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 504 apples and 12 baskets. How will they divide it equally?
They will get 42 apples each.
To divide the apples equally, we need to divide the total apples by the number of baskets. 504/12 = 42
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.
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.
There are 42 teams and 504 players. How many players will be in each team?
Each team will have 12 players.
To find the players in each team, divide the total players by the number of teams. 504/42 = 12
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.
Dividing the people by the total groups, we will get the number of people in each group. 504/7 = 72
504 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 84 books.
Divide total books by shelves. 504/6 = 84
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.
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.
: She loves to read number jokes and games.