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Last updated on May 26th, 2025

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Factors of 1512

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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 1512, how they are used in real life, and the tips to learn them quickly.

Factors of 1512 for Omani Students
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What are the Factors of 1512?

The numbers that divide 1512 evenly are known as factors of 1512.

 

A factor of 1512 is a number that divides the number without a remainder.

 

The factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512.

 

Negative factors of 1512: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -27, -28, -36, -42, -54, -56, -63, -72, -84, -108, -126, -168, -189, -216, -252, -378, -504, -756, and -1512.

 

Prime factors of 1512: 2, 3, and 7.

 

Prime factorization of 1512: 23 × 33 × 7.

 

The sum of factors of 1512: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 27 + 28 + 36 + 42 + 54 + 56 + 63 + 72 + 84 + 108 + 126 + 168 + 189 + 216 + 252 + 378 + 504 + 756 + 1512 = 4423

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How to Find Factors of 1512?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1512. Identifying the numbers which are multiplied to get the number 1512 is the multiplication method.

 

Step 1: Multiply 1512 by 1, 1512 × 1 = 1512.

 

Step 2: Check for other numbers that give 1512 after multiplying

2 × 756 = 1512

3 × 504 = 1512

4 × 378 = 1512

6 × 252 = 1512

7 × 216 = 1512

9 × 168 = 1512

12 × 126 = 1512

14 × 108 = 1512

18 × 84 = 1512

21 × 72 = 1512

24 × 63 = 1512

27 × 56 = 1512

28 × 54 = 1512

36 × 42 = 1512

 

Therefore, the positive factor pairs of 1512 are: (1, 1512), (2, 756), (3, 504), (4, 378), (6, 252), (7, 216), (8, 189), (9, 168), (12, 126), (14, 108), (18, 84), (21, 72), (24, 63), (27, 56), (28, 54), and (36, 42).

 

For every positive factor, there is a negative factor.

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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 1512 by 1, 1512 ÷ 1 = 1512.

 

Step 2: Continue dividing 1512 by the numbers until the remainder becomes 0.

1512 ÷ 1 = 1512

1512 ÷ 2 = 756

1512 ÷ 3 = 504

1512 ÷ 4 = 378

1512 ÷ 6 = 252

1512 ÷ 7 = 216

1512 ÷ 8 = 189

1512 ÷ 9 = 168

1512 ÷ 12 = 126

1512 ÷ 14 = 108

1512 ÷ 18 = 84

1512 ÷ 21 = 72

1512 ÷ 24 = 63

1512 ÷ 27 = 56

1512 ÷ 28 = 54

1512 ÷ 36 = 42

 

Therefore, the factors of 1512 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512.

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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 1512 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

1512 ÷ 2 = 756

756 ÷ 2 = 378

378 ÷ 2 = 189

189 ÷ 3 = 63

63 ÷ 3 = 21

21 ÷ 3 = 7

7 ÷ 7 = 1

 

The prime factors of 1512 are 2, 3, and 7.

 

The prime factorization of 1512 is: 23 × 33 × 7.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

 

Step 1: Firstly, 1512 is divided by 2 to get 756.

 

Step 2: Now divide 756 by 2 to get 378.

 

Step 3: Then divide 378 by 2 to get 189.

 

Step 4: Divide 189 by 3 to get 63.

 

Step 5: Divide 63 by 3 to get 21.

 

Step 6: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1512 is: 23 × 33 × 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 1512: (1, 1512), (2, 756), (3, 504), (4, 378), (6, 252), (7, 216), (8, 189), (9, 168), (12, 126), (14, 108), (18, 84), (21, 72), (24, 63), (27, 56), (28, 54), and (36, 42).

 

Negative factor pairs of 1512: (-1, -1512), (-2, -756), (-3, -504), (-4, -378), (-6, -252), (-7, -216), (-8, -189), (-9, -168), (-12, -126), (-14, -108), (-18, -84), (-21, -72), (-24, -63), (-27, -56), (-28, -54), and (-36, -42).

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Common Mistakes and How to Avoid Them in Factors of 1512

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

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Forgetting the number itself and 1 is a factor

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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 1512, 1 and 1512 are also factors.

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Factors of 1512 Examples

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Problem 1

A teacher has 1512 pencils and wants to distribute them equally among 7 classes. How many pencils will each class get?

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Each class will get 216 pencils.

Explanation

To divide the pencils equally, we need to divide the total pencils by the number of classes.

1512/7 = 216

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Problem 2

A rectangular garden has an area of 1512 square meters and a width of 18 meters. What is the length of the garden?

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The length of the garden is 84 meters.

Explanation

To find the length of the garden, we use the formula, Area = length × width

1512 = length × 18

To find the value of length, we need to divide 1512 by 18.

1512/18 = length

Length = 84.

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Problem 3

There are 9 teams in a tournament, and 1512 medals are to be distributed equally. How many medals will each team receive?

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Each team will receive 168 medals.

Explanation

To find the medals each team receives, divide the total medals by the number of teams.     

1512/9 = 168

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Problem 4

A library has 1512 books, and they need to be arranged in 27 equal stacks. How many books will each stack have?

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Each stack will have 56 books.

Explanation

Divide the total books by the number of stacks to find the number of books in each stack.    

1512/27 = 56

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Problem 5

A baker has 1512 cookies and wants to pack them in boxes containing 42 cookies each. How many boxes will be needed?

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36 boxes will be needed.

Explanation

To find the number of boxes needed, divide the total cookies by the number of cookies per box.     

1512/42 = 36

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FAQs on Factors of 1512

1.What are the factors of 1512?

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2.Mention the prime factors of 1512.

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3.Is 1512 a multiple of 9?

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4.Mention the factor pairs of 1512?

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5.What is the square of 1512?

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6.How can children in Oman use numbers in everyday life to understand Factors of 1512?

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7.What are some fun ways kids in Oman can practice Factors of 1512 with numbers?

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8.What role do numbers and Factors of 1512 play in helping children in Oman develop problem-solving skills?

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9.How can families in Oman create number-rich environments to improve Factors of 1512 skills?

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Important Glossaries for Factors of 1512

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 1512.

 

  • 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 1512 are (1, 1512), (2, 756), etc.

 

  • Prime factorization: The expression of a number as the product of its prime factors. The prime factorization of 1512 is 23 × 33 × 7.

 

  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number, such as (6, 252) for 1512.
Professor Greenline from BrightChamps

About BrightChamps in Oman

At BrightChamps, numbers mean more than just digits—they open doors to many opportunities! We’re committed to helping children across Oman build important math skills, with today’s focus on Factors of 1512 and a special spotlight on factors—in a lively, clear, and fun way. Whether your child is calculating the speed of a ride at Oman’s Dreamland Aqua Park, keeping score at football matches, or managing their allowance for gadgets, mastering numbers boosts their confidence daily. Our engaging lessons make learning simple and enjoyable. Since kids in Oman learn differently, we adapt lessons to each learner. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps makes math come alive across Oman. Let’s turn factors into a fun part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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