117 LearnersLast updated on May 26th, 2025
Factors of 1632
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 1632, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1632?
The numbers that divide 1632 evenly are known as factors of 1632.
A factor of 1632 is a number that divides the number without remainder.
The factors of 1632 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 544, 816, and 1632.
Negative factors of 1632: -1, -2, -3, -4, -6, -8, -12, -16, -24, -34, -48, -51, -68, -102, -136, -204, -272, -408, -544, -816, and -1632.
Prime factors of 1632: 2 and 3.
Prime factorization of 1632: (24 times 3 times 17).
The sum of factors of 1632: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 34 + 48 + 51 + 68 + 102 + 136 + 204 + 272 + 408 + 544 + 816 + 1632 = 4320
How to Find Factors of 1632?
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 1632. Identifying the numbers which are multiplied to get the number 1632 is the multiplication method.
Step 1: Multiply 1632 by 1, 1632 × 1 = 1632.
Step 2: Check for other numbers that give 1632 after multiplying
2 × 816 = 1632
3 × 544 = 1632
4 × 408 = 1632
6 × 272 = 1632
8 × 204 = 1632
12 × 136 = 1632
16 × 102 = 1632
24 × 68 = 1632
34 × 48 = 1632
Therefore, the positive factor pairs of 1632 are: (1, 1632), (2, 816), (3, 544), (4, 408), (6, 272), (8, 204), (12, 136), (16, 102), (24, 68), (34, 48).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1632 by 1, 1632 ÷ 1 = 1632.
Step 2: Continue dividing 1632 by the numbers until the remainder becomes 0.
1632 ÷ 1 = 1632
1632 ÷ 2 = 816
1632 ÷ 3 = 544
1632 ÷ 4 = 408
1632 ÷ 6 = 272
1632 ÷ 8 = 204
1632 ÷ 12 = 136
1632 ÷ 16 = 102
1632 ÷ 24 = 68
1632 ÷ 34 = 48
Therefore, the factors of 1632 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 544, 816, 1632.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1632 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1632 ÷ 2 = 816
816 ÷ 2 = 408
408 ÷ 2 = 204
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 1632 are 2, 3, and 17. The prime factorization of 1632 is: (24 times 3 times 17).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1632 is divided by 2 to get 816.
Step 2: Now divide 816 by 2 to get 408.
Step 3: Then divide 408 by 2 to get 204.
Step 4: Divide 204 by 2 to get 102.
Step 5: Divide 102 by 2 to get 51.
Step 6: Divide 51 by 3 to get 17.
Step 7: Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1632 is: (24 times 3 times 17).
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 1632: (1, 1632), (2, 816), (3, 544), (4, 408), (6, 272), (8, 204), (12, 136), (16, 102), (24, 68), (34, 48).
Negative factor pairs of 1632: (-1, -1632), (-2, -816), (-3, -544), (-4, -408), (-6, -272), (-8, -204), (-12, -136), (-16, -102), (-24, -68), (-34, -48).
Common Mistakes and How to Avoid Them in Factors of 1632
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 as Factors
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 1632, 1 and 1632 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1632 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1632/1.5 does not yield 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 1632 are prime numbers. For example, 2 and 3 are the prime factors of 1632, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1632 as (24 times 3 times 17) and missing all the key factors.
Factors of 1632 Examples
Problem 1
There are 34 students and 1632 candies. How will they divide them equally?
They will get 48 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1632/34 = 48
Problem 2
A parking lot is rectangular, the length of the lot is 34 meters, and the total area is 1632 square meters. Find the width.
48 meters.
Explanation
To find the width of the lot, we use the formula, Area = length × width
1632 = 34 × width
To find the value of the width, we need to shift 34 to the left side.
1632/34 = width
Width = 48
Problem 3
There are 102 boxes and 1632 apples. How many apples will be in each box?
Each box will have 16 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1632/102 = 16
Problem 4
In a school, there are 136 students and 1632 books. How many books are there for each student?
There are 12 books for each student.
Explanation
Dividing the books by the total students, we will get the number of books for each student.
1632/136 = 12
Problem 5
1632 pages need to be distributed equally among 54 folders. How many pages will go in each folder?
Each folder will have 30 pages.
Explanation
Divide total pages by folders.
1632/54 = 30
FAQs on Factors of 1632
1.What are the factors of 1632?
2.Mention the prime factors of 1632.
3.Is 1632 a multiple of 6?
4.Mention the factor pairs of 1632?
5.What is the square of 1632?
6.How can children in United States use numbers in everyday life to understand Factors of 1632?
7.What are some fun ways kids in United States can practice Factors of 1632 with numbers?
8.What role do numbers and Factors of 1632 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1632 skills?
Important Glossaries for Factors of 1632
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1632 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 544, 816, and 1632.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 1632.
- 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 1632 are (1, 1632), (2, 816), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 1632 is (24 times 3 times 17).
- Multiplication method: A method to find factors by identifying numbers that multiply to give the original number.
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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.
