116 LearnersLast updated on June 2nd, 2025
Factors of 4032
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 4032, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 4032?
The numbers that divide 4032 evenly are known as factors of 4032.
A factor of 4032 is a number that divides the number without remainder.
The factors of 4032 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 576, 672, 1008, 1344, 2016, and 4032.
Negative factors of 4032: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -32, -36, -42, -48, -56, -63, -72, -84, -96, -112, -126, -144, -168, -224, -252, -288, -336, -504, -576, -672, -1008, -1344, -2016, and -4032.
Prime factors of 4032: 2, 3, and 7.
Prime factorization of 4032: 25 × 32 × 72.
The sum of factors of 4032: 10920.
How to Find Factors of 4032?
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 4032. Identifying the numbers which are multiplied to get the number 4032 is the multiplication method.
Step 1: Multiply 4032 by 1, 4032 × 1 = 4032.
Step 2: Check for other numbers that give 4032 after multiplying
2 × 2016 = 4032
3 × 1344 = 4032
4 × 1008 = 4032
6 × 672 = 4032
7 × 576 = 4032
8 × 504 = 4032
9 × 448 = 4032
12 × 336 = 4032
14 × 288 = 4032
16 × 252 = 4032
18 × 224 = 4032
21 × 192 = 4032
24 × 168 = 4032
28 × 144 = 4032
32 × 126 = 4032
36 × 112 = 4032
42 × 96 = 4032
48 × 84 = 4032
56 × 72 = 4032
Therefore, the positive factor pairs of 4032 are: (1, 4032), (2, 2016), (3, 1344), (4, 1008), (6, 672), (7, 576), (8, 504), (9, 448), (12, 336), (14, 288), (16, 252), (18, 224), (21, 192), (24, 168), (28, 144), (32, 126), (36, 112), (42, 96), (48, 84), and (56, 72).
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 the simple division method
Step 1: Divide 4032 by 1, 4032 ÷ 1 = 4032.
Step 2: Continue dividing 4032 by the numbers until the remainder becomes 0.
4032 ÷ 1 = 4032
4032 ÷ 2 = 2016
4032 ÷ 3 = 1344
4032 ÷ 4 = 1008
4032 ÷ 6 = 672
4032 ÷ 7 = 576
4032 ÷ 8 = 504
4032 ÷ 9 = 448
4032 ÷ 12 = 336
4032 ÷ 14 = 288
4032 ÷ 16 = 252
4032 ÷ 18 = 224
4032 ÷ 21 = 192
4032 ÷ 24 = 168
4032 ÷ 28 = 144
4032 ÷ 32 = 126
4032 ÷ 36 = 112
4032 ÷ 42 = 96
4032 ÷ 48 = 84
4032 ÷ 56 = 72
Therefore, the factors of 4032 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 576, 672, 1008, 1344, 2016, and 4032.
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 4032 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
4032 ÷ 2 = 2016
2016 ÷ 2 = 1008
1008 ÷ 2 = 504
504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 3 = 42
42 ÷ 3 = 14
14 ÷ 7 = 2
2 ÷ 2 = 1
The prime factors of 4032 are 2, 3, and 7.
The prime factorization of 4032 is: 25 × 32 × 72.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 4032 is divided by 2 to get 2016.
Step 2: Now divide 2016 by 2 to get 1008.
Step 3: Then divide 1008 by 2 to get 504.
Step 4: Divide 504 by 2 to get 252.
Step 5: Divide 252 by 2 to get 126.
Step 6: Divide 126 by 3 to get 42.
Step 7: Divide 42 by 3 to get 14.
Step 8: Divide 14 by 7 to get 2. Here, 2 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 4032 is: 25 × 32 × 72.
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 4032: (1, 4032), (2, 2016), (3, 1344), (4, 1008), (6, 672), (7, 576), (8, 504), (9, 448), (12, 336), (14, 288), (16, 252), (18, 224), (21, 192), (24, 168), (28, 144), (32, 126), (36, 112), (42, 96), (48, 84), and (56, 72).
Negative factor pairs of 4032: (-1, -4032), (-2, -2016), (-3, -1344), (-4, -1008), (-6, -672), (-7, -576), (-8, -504), (-9, -448), (-12, -336), (-14, -288), (-16, -252), (-18, -224), (-21, -192), (-24, -168), (-28, -144), (-32, -126), (-36, -112), (-42, -96), (-48, -84), and (-56, -72).
Common Mistakes and How to Avoid Them in Factors of 4032
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 4032, 1 and 4032 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 4032 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 4032/1.5 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 4032 are prime numbers. For example, 2, 3, and 7 are the prime factors of 4032, but it has other factors like 4, 6, and 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 4032 as 25 × 32 × 72 and missing all the key factors.
Factors of 4032 Examples
Problem 1
A baker has 4032 cookies and wants to pack them evenly into boxes. If he packs 56 cookies per box, how many boxes does he need?
He will need 72 boxes.
Explanation
To find the number of boxes needed, divide the total cookies by the cookies per box.
4032/56 = 72
Problem 2
A rectangular garden has an area of 4032 square meters. If the length of the garden is 84 meters, what is the width?
48 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
4032 = 84 × width
To find the value of width, we need to shift 84 to the left side.
4032/84 = width
Width = 48.
Problem 3
A theater has 2016 seats and they want to divide them into sections with 12 seats each. How many sections will there be?
There will be 168 sections.
Explanation
To find the number of sections, divide the total seats by seats per section.
2016/12 = 168
Problem 4
A company has 4032 employees and wants to form teams with 42 employees each. How many teams can they form?
They can form 96 teams.
Explanation
Dividing the employees by the total team members, we will get the number of teams.
4032/42 = 96
Problem 5
There are 4032 pages to be printed, and a printer prints 7 pages per minute. How long will it take to print all the pages?
It will take 576 minutes.
Explanation
Divide total pages by pages per minute.
4032/7 = 576
FAQs on Factors of 4032
1.What are the factors of 4032?
2.Mention the prime factors of 4032.
3.Is 4032 a multiple of 8?
4.Mention the factor pairs of 4032?
5.What is the square of 4032?
Important Glossaries for Factors of 4032
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 4032 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 4032.
- 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 4032 are (1, 4032), (2, 2016), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 4032 is 25 × 32 × 72.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, using the multiplication method to find factors of 4032.
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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.
