118 LearnersLast updated on May 26th, 2025
Factors of 3400
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 3400, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3400?
The numbers that divide 3400 evenly are known as factors of 3400.
A factor of 3400 is a number that divides the number without a remainder.
The factors of 3400 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, and 3400.
Negative factors of 3400: -1, -2, -4, -5, -10, -17, -20, -25, -34, -50, -68, -85, -100, -136, -170, -200, -340, -425, -680, -850, -1700, and -3400.
Prime factors of 3400: 2, 5, and 17.
Prime factorization of 3400: 22 × 52 × 17.
The sum of the factors of 3400: 1 + 2 + 4 + 5 + 10 + 17 + 20 + 25 + 34 + 50 + 68 + 85 + 100 + 136 + 170 + 200 + 340 + 425 + 680 + 850 + 1700 + 3400 = 8352
How to Find Factors of 3400?
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 3400. Identifying the numbers which are multiplied to get the number 3400 is the multiplication method.
Step 1: Multiply 3400 by 1, 3400 × 1 = 3400.
Step 2: Check for other numbers that give 3400 after multiplying
2 × 1700 = 3400
4 × 850 = 3400
5 × 680 = 3400
10 × 340 = 3400
20 × 170 = 3400
25 × 136 = 3400
34 × 100 = 3400
50 × 68 = 3400
Therefore, the positive factor pairs of 3400 are: (1, 3400), (2, 1700), (4, 850), (5, 680), (10, 340), (20, 170), (25, 136), (34, 100), (50, 68). 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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 3400 by 1, 3400 ÷ 1 = 3400.
Step 2: Continue dividing 3400 by the numbers until the remainder becomes 0.
3400 ÷ 1 = 3400
3400 ÷ 2 = 1700
3400 ÷ 4 = 850
3400 ÷ 5 = 680
3400 ÷ 10 = 340
3400 ÷ 20 = 170
3400 ÷ 25 = 136
3400 ÷ 34 = 100
3400 ÷ 50 = 68
Therefore, the factors of 3400 are: 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400.
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 3400 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3400 ÷ 2 = 1700
1700 ÷ 2 = 850
850 ÷ 2 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 3400 are 2, 5, and 17.
The prime factorization of 3400 is: 2^2 × 5^2 × 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, 3400 is divided by 2 to get 1700.
Step 2: Now divide 1700 by 2 to get 850.
Step 3: Then divide 850 by 2 to get 425.
Step 4: Divide 425 by 5 to get 85.
Step 5: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3400 is: 2^2 × 5^2 × 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 3400: (1, 3400), (2, 1700), (4, 850), (5, 680), (10, 340), (20, 170), (25, 136), (34, 100), and (50, 68).
Negative factor pairs of 3400: (-1, -3400), (-2, -1700), (-4, -850), (-5, -680), (-10, -340), (-20, -170), (-25, -136), (-34, -100), and (-50, -68).
Common Mistakes and How to Avoid Them in Factors of 3400
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 3400, 1 and 3400 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 3400 consist of -1, -2, -4, 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 3400/1.5 = 2266.666, 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 3400 are prime numbers.
For example, 2, 5, and 17 are the prime factors of 3400, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3400 as 2^2 × 5^2 × 17 and missing all the key factors.
Factors of 3400 Examples
Problem 1
A charity wants to distribute 3400 meals equally among 10 shelters. How many meals will each shelter receive?
Each shelter will receive 340 meals.
Explanation
To divide the meals equally, we need to divide the total meals by the number of shelters.
3400/10 = 340
Problem 2
A rectangular park has a length of 50 meters and a total area of 3400 square meters. Find the width.
68 meters.
Explanation
To find the width of the park, we use the formula,
Area = length × width
3400 = 50 × width
To find the value of width, we need to shift 50 to the left side.
3400/50 = width
Width = 68.
Problem 3
There are 3400 chairs, and they need to be arranged in 100 rows. How many chairs will be in each row?
Each row will have 34 chairs.
Explanation
To find the number of chairs in each row, divide the total chairs by the number of rows.
3400/100 = 34
Problem 4
In a company, there are 3400 employees and 50 departments. How many employees are there in each department?
There are 68 employees in each department.
Explanation
Dividing the employees by the total departments, we will get the number of employees in each department.
3400/50 = 68
Problem 5
A library has 3400 books to be arranged on 200 shelves. How many books will go on each shelf?
Each of the shelves has 17 books.
Explanation
Divide total books by shelves.
3400/200 = 17
FAQs on Factors of 3400
1.What are the factors of 3400?
2.Mention the prime factors of 3400.
3.Is 3400 a multiple of 5?
4.Mention the factor pairs of 3400?
5.What is the square of 3400?
Important Glossaries for Factor of 3400
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3400 are 1, 2, 4, 5, 10, 17, 20, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 3400.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 3400 is 22 × 52 × 17.
- 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 3400 are (1, 3400), (2, 1700), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give a particular product.
Explore More numbers
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.
