126 LearnersLast updated on May 26th, 2025
Factors of 578
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 578, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 578?
The numbers that divide 578 evenly are known as factors of 578.
A factor of 578 is a number that divides the number without remainder.
The factors of 578 are 1, 2, 17, 34, 289, and 578.
Negative factors of 578: -1, -2, -17, -34, -289, and -578.
Prime factors of 578: 2 and 17.
Prime factorization of 578: 2 × 17 × 17.
The sum of factors of 578: 1 + 2 + 17 + 34 + 289 + 578 = 921
How to Find Factors of 578?
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 578. Identifying the numbers which are multiplied to get the number 578 is the multiplication method.
Step 1: Multiply 578 by 1, 578 × 1 = 578.
Step 2: Check for other numbers that give 578 after multiplying
2 × 289 = 578
17 × 34 = 578
Therefore, the positive factor pairs of 578 are: (1, 578), (2, 289), (17, 34). All these factor pairs result in 578. 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 578 by 1, 578 ÷ 1 = 578.
Step 2: Continue dividing 578 by the numbers until the remainder becomes 0.
578 ÷ 1 = 578
578 ÷ 2 = 289
578 ÷ 17 = 34
Therefore, the factors of 578 are: 1, 2, 17, 34, 289, 578.
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 578 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
578 ÷ 2 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
The prime factors of 578 are 2 and 17.
The prime factorization of 578 is: 2 × 17 × 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, 578 is divided by 2 to get 289.
Step 2: Now divide 289 by 17 to get 17.
Step 3: Here, 17 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 578 is: 2 × 17 × 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 578: (1, 578), (2, 289), (17, 34).
Negative factor pairs of 578: (-1, -578), (-2, -289), (-17, -34).
Common Mistakes and How to Avoid Them in Factors of 578
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 578, 1 and 578 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 578 consist of -1, -2, -17, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 578/1.5 ≈ 385.33, and it 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 578 are prime numbers.
For example, 2 and 17 are the prime factors of 578, but it has other factors like 34, 289.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 578 as 2 × 17 × 17 and missing key factors.
Factors of 578 Examples
Problem 1
There are 17 gift bags, and 578 candies. How will they distribute it equally?
They will get 34 candies each.
Explanation
To distribute the candies equally, we need to divide the total candies by the number of gift bags.
578/17 = 34
Problem 2
A garden is rectangular, the length of the garden is 2 meters and the total area is 578 square meters. Find the width?
289 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
578 = 2 × width
To find the value of width, we need to shift 2 to the left side.
578/2 = width
Width = 289.
Problem 3
There are 34 boxes and 578 apples. How many apples will be in each box?
Each box will have 17 apples.
Explanation
To find the apples in each box, divide the total apples by the number of boxes.
578/34 = 17
Problem 4
In a class, there are 578 students, and 289 rows. How many students are there in each row?
There are 2 students in each row.
Explanation
Dividing the students by the total rows, we will get the number of students in each row.
578/289 = 2
Problem 5
578 books need to be arranged in 289 shelves. How many books will go on each shelf?
Each shelf has 2 books.
Explanation
Divide total books by shelves. 578/289 = 2
FAQs on Factors of 578
1.What are the factors of 578?
2.Mention the prime factors of 578.
3.Is 578 a multiple of 17?
4.Mention the factor pairs of 578?
5.What is the square of 578?
Important Glossaries for Factors of 578
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 578 are 1, 2, 17, 34, 289, and 578.
- Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of 578.
- 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 578 are (1, 578), (2, 289), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 578 is 2 × 17 × 17.
- Negative factors: Numbers that are negative and divide the given number without leaving a remainder. For example, the negative factors of 578 are -1, -2, -17, -34, -289, and -578.
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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.
