116 LearnersLast updated on May 26th, 2025
Factors of 4608
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 4608, how they are used in real life, and tips to learn them quickly.
What are the Factors of 4608?
The numbers that divide 4608 evenly are known as factors of 4608.
A factor of 4608 is a number that divides the number without a remainder.
The factors of 4608 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 768, 1152, 2304, and 4608.
Negative factors of 4608: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -288, -384, -576, -768, -1152, -2304, and -4608.
Prime factors of 4608: 2 and 3. Prime factorization of 4608: 28 × 32.
The sum of factors of 4608: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 288 + 384 + 576 + 768 + 1152 + 2304 + 4608 = 12480
How to Find Factors of 4608?
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 4608. Identifying the numbers which are multiplied to get the number 4608 is the multiplication method.
Step 1: Multiply 4608 by 1, 4608 × 1 = 4608.
Step 2: Check for other numbers that give 4608 after multiplying
2 × 2304 = 4608
3 × 1536 = 4608
4 × 1152 = 4608
6 × 768 = 4608 ...and so on.
Therefore, the positive factor pairs of 4608 include: (1, 4608), (2, 2304), (3, 1536), (4, 1152), (6, 768), etc.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 4608 by 1, 4608 ÷ 1 = 4608.
Step 2: Continue dividing 4608 by the numbers until the remainder becomes 0.
4608 ÷ 1 = 4608
4608 ÷ 2 = 2304
4608 ÷ 3 = 1536
4608 ÷ 4 = 1152
4608 ÷ 6 = 768 ...and so on.
Therefore, the factors of 4608 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 768, 1152, 2304, 4608.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 4608 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
4608 ÷ 2 = 2304
2304 ÷ 2 = 1152
1152 ÷ 2 = 576
576 ÷ 2 = 288
288 ÷ 2 = 144
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 3 = 6
6 ÷ 3 = 2
The prime factors of 4608 are 2 and 3.
The prime factorization of 4608 is: 28 × 32.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 4608 is divided by 2 to get 2304.
Step 2: Now divide 2304 by 2 to get 1152.
Step 3: Then divide 1152 by 2 to get 576.
Step 4: Continue the division process until you reach a prime number. So, the prime factorization of 4608 is: 28 × 32.
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 4608: (1, 4608), (2, 2304), (3, 1536), (4, 1152), (6, 768), etc.
Negative factor pairs of 4608: (-1, -4608), (-2, -2304), (-3, -1536), (-4, -1152), (-6, -768), etc.
Common Mistakes and How to Avoid Them in Factors of 4608
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 4608, 1 and 4608 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 4608 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 4608/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 4608 are prime numbers. For instance, 2 and 3 are the prime factors of 4608, but it has other factors like 4, 9, 12, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not breaking 4608 correctly into 28 × 32 and missing key factors.
Factors of 4608 Examples
Problem 1
A music concert has 4608 attendees, and each row can accommodate 128 people. How many rows are needed?
36 rows.
Explanation
To find the number of rows needed, divide the total attendees by the number of people each row can accommodate.
4608/128 = 36
Problem 2
A tile company has 4608 tiles, and they want to create square areas. What is the largest side length they can use?
72.
Explanation
The largest side length is the greatest factor of 4608 that is a perfect square, which is 72. 72 × 72 = 5184, which is a factor of 4608.
Problem 3
There are 4608 apples, and they need to be packed in boxes containing 192 apples each. How many boxes are needed?
24 boxes.
Explanation
To find the number of boxes needed, divide the total apples by the number of apples each box can contain.
4608/192 = 24
Problem 4
A hall has a capacity of 4608 seats, and they are arranged in 384 rows. How many seats are there per row?
12 seats.
Explanation
Dividing the total seats by the number of rows, we get the number of seats per row.
4608/384 = 12
Problem 5
4608 books need to be evenly distributed among 576 shelves. How many books will go on each shelf?
8 books.
Explanation
Divide the total number of books by the number of shelves.
4608/576 = 8
FAQs on Factors of 4608
1.What are the factors of 4608?
2.Mention the prime factors of 4608.
3.Is 4608 a multiple of 9?
4.Mention the factor pairs of 4608?
5.What is the square root of 4608 approximated to the nearest whole number?
Important Glossaries for Factors of 4608
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 4608 include 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 4608.
- 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 4608 include (1, 4608), (2, 2304), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 4608 is 28 × 32.
- Multiple: A number that can be divided by another number without a remainder. For example, 4608 is a multiple of 9.
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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.
