125 LearnersLast updated on May 26th, 2025
Factors of 340
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 340, how they are used in real life, and tips to learn them quickly.
What are the Factors of 340?
The numbers that divide 340 evenly are known as factors of 340.
A factor of 340 is a number that divides the number without remainder.
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340.
Negative factors of 340: -1, -2, -4, -5, -10, -17, -20, -34, -68, -85, -170, and -340.
Prime factors of 340: 2, 5, and 17.
Prime factorization of 340: 2² × 5 × 17.
The sum of factors of 340: 1 + 2 + 4 + 5 + 10 + 17 + 20 + 34 + 68 + 85 + 170 + 340 = 756
How to Find Factors of 340?
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 340. Identifying the numbers which are multiplied to get the number 340 is the multiplication method.
Step 1: Multiply 340 by 1, 340 × 1 = 340.
Step 2: Check for other numbers that give 340 after multiplying
2 × 170 = 340
4 × 85 = 340
5 × 68 = 340
10 × 34 = 340
17 × 20 = 340
Therefore, the positive factor pairs of 340 are: (1, 340), (2, 170), (4, 85), (5, 68), (10, 34), (17, 20).
All these factor pairs result in 340.
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 the simple division method
Step 1: Divide 340 by 1, 340 ÷ 1 = 340.
Step 2: Continue dividing 340 by the numbers until the remainder becomes 0.
340 ÷ 1 = 340
340 ÷ 2 = 170
340 ÷ 4 = 85
340 ÷ 5 = 68
340 ÷ 10 = 34
340 ÷ 17 = 20
Therefore, the factors of 340 are: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340.
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 340 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
340 ÷ 2 = 170
170 ÷ 2 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 340 are 2, 5, and 17.
The prime factorization of 340 is: 2² × 5 × 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, 340 is divided by 2 to get 170.
Step 2: Now divide 170 by 2 to get 85.
Step 3: Then divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 340 is: 2² × 5 × 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 340: (1, 340), (2, 170), (4, 85), (5, 68), (10, 34), and (17, 20).
Negative factor pairs of 340: (-1, -340), (-2, -170), (-4, -85), (-5, -68), (-10, -34), and (-17, -20).
Common Mistakes and How to Avoid Them in Factors of 340
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 word. Always remember to include 1 and the number itself.
For example, in factors of 340, 1 and 340 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 340 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 340/1.5 ≈ 226.667, 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 340 are prime numbers.
For example, 2, 5, and 17 are the prime factors of 340, but it has other factors like 10, 34.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 340 as 2² × 5 × 17 and missing all the key factors.
Factors of 340 Examples
Problem 1
There are 10 cakes and 340 pieces of decoration. How will they divide the decorations equally?
They will get 34 pieces of decoration each.
Explanation
To divide the decorations equally, we need to divide the total pieces with the number of cakes.
340/10 = 34
Problem 2
A hall is rectangular, the length of the hall is 20 meters and the total area is 340 square meters. Find the width.
17 meters.
Explanation
To find the width of the hall, we use the formula,
Area = length × width
340 = 20 × width
To find the value of width, we need to shift 20 to the left side.
340/20 = width
Width = 17.
Problem 3
There are 34 boxes and 340 pens. How many pens will be in each box?
Each box will have 10 pens.
Explanation
To find the pens in each box, divide the total pens with the boxes.
340/34 = 10
Problem 4
In a club, there are 340 members, and 5 teams. How many members are there in each team?
There are 68 members in each team.
Explanation
Dividing the members with the total teams, we will get the number of members in each team.
340/5 = 68
Problem 5
340 plants need to be arranged in 17 rows. How many plants will go in each row?
Each row will have 20 plants.
Explanation
Divide total plants with rows.
340/17 = 20
FAQs on Factors of 340
1.What are the factors of 340?
2.Mention the prime factors of 340.
3.Is 340 a multiple of 5?
4.Mention the factor pairs of 340?
5.What is the square of 340?
6.How can children in Qatar use numbers in everyday life to understand Factors of 340?
7.What are some fun ways kids in Qatar can practice Factors of 340 with numbers?
8.What role do numbers and Factors of 340 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 340 skills?
Important Glossaries for Factors of 340
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 340.
- 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 340 are (1, 340), (2, 170), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 340 is 2² × 5 × 17.
- Multiples: A multiple of a number is the product of that number and an integer. For example, 340 is a multiple of 5.
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About BrightChamps in Qatar
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.
