121 LearnersLast updated on May 26th, 2025
Factors of 1512
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.
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
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
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.
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.
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.
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).
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
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 1512, 1 and 1512 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 1512 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 1512/1.5 = 1008, 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 1512 are prime numbers. For example, 2, 3, and 7 are the prime factors of 1512, but it has other factors like 4, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1512 as 23 × 33 × 7 and missing all the key factors.
Factors of 1512 Examples
Problem 1
A teacher has 1512 pencils and wants to distribute them equally among 7 classes. How many pencils will each class get?
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
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?
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.
Problem 3
There are 9 teams in a tournament, and 1512 medals are to be distributed equally. How many medals will each team receive?
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
Problem 4
A library has 1512 books, and they need to be arranged in 27 equal stacks. How many books will each stack have?
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
Problem 5
A baker has 1512 cookies and wants to pack them in boxes containing 42 cookies each. How many boxes will be needed?
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
FAQs on Factors of 1512
1.What are the factors of 1512?
2.Mention the prime factors of 1512.
3.Is 1512 a multiple of 9?
4.Mention the factor pairs of 1512?
5.What is the square of 1512?
6.How can children in Oman use numbers in everyday life to understand Factors of 1512?
7.What are some fun ways kids in Oman can practice Factors of 1512 with numbers?
8.What role do numbers and Factors of 1512 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of 1512 skills?
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.
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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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