Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A charity wants to distribute 3400 meals equally among 10 shelters. How many meals will each shelter receive?
Each shelter will receive 340 meals.
To divide the meals equally, we need to divide the total meals by the number of shelters.
3400/10 = 340
A rectangular park has a length of 50 meters and a total area of 3400 square meters. Find the width.
68 meters.
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.
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.
To find the number of chairs in each row, divide the total chairs by the number of rows.
3400/100 = 34
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.
Dividing the employees by the total departments, we will get the number of employees in each department.
3400/50 = 68
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.
Divide total books by shelves.
3400/200 = 17
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.
: She loves to read number jokes and games.