337 LearnersLast updated on May 26th, 2025
Factors of 342
Factors of 342 are numbers that can divide 342 completely without leaving a remainder. We often use factors for organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 342 and the different methods to find them.
What are the Factors of 342?
The factors of 342 are the numbers that divide 342 evenly.
Positive Factors: These are the positive numbers that divide 342 evenly.
Positive factors are 1, 2, 3, 6, 57, 114, 171, and 342.
Negative Factors: These are the negative counterparts of the positive factors.
Negative factors are -1, -2, -3, -6, -57, -114, -171, -342
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 342 as the product.
Prime factors: 2, 3, 19
Prime Factorization: Prime factorization involves breaking 342 into its prime factors.
It is expressed as 21 × 32 × 192
Table listing the factors of 342
|
Positive Factors |
1, 2, 3, 6, 57, 114, 171, 342 |
|
Negative Factors |
-1, -2, -3, -6, -57, -114, -171, -342 |
|
Prime Factors |
2, 3, 19 |
|
Prime Factorization |
21 × 32 × 192 |
This breakdown helps in understanding the various factors of 342, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 342?
There are different methods to find the factors of 342.
Methods to find the factors of 342:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 342 as their product.
Step 1: Find the pair of numbers whose product is 342.
Step 2: The factors are those numbers that, when multiplied, give 342.
Step 3: Make a list of numbers whose product will be 342.
A list of numbers whose products are 342 is given below:
- 1 × 342 = 342
- 2 × 171 = 342
- 3 × 114 = 342
- 6 × 57 = 342
Thus, the factors of 342 are 1, 2, 3, 6, 57, 114, 171, and 342.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 342÷1=342
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 342 are 1, 2, 3, 6, 57, 114, 171, and 342.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number, when it is simplified using the factors of that number and is expressed in the form of prime factors, is the prime factorization of a number.
Prime Factors of 342: Number 342 has three prime factors.
Prime factors of 342: 2, 3, 19
To find the prime factors of 342, we can divide 342 with the prime numbers like 2, 3, and 19 from the list of factors of 342.
Step 1: Divide 342 with the prime number 2: 342÷2=171
Step 2: Divide 171 with the prime number 3: 171÷3=57
Step 3: Divide 57 with the prime number 3: 57÷3=19
Step 4: Divide 19 with the prime number 19: 19÷19=1
Prime Factorization of 342: Prime factorization breaks down the prime factors of 342.
Expressed as 21 × 32 × 192
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.
This tree shows the breakdown of 342 into its prime factors: 2 × 3 × 19.
Positive and Negative Factor Pairs of 342
Factors of 342 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1, 342), (2, 171), (3, 114), (6, 57)
Negative Factor Pairs: (-1, -342), (-2, -171), (-3, -114), (-6, -57)
Common Mistakes and How to Avoid Them in Factors of 342
Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming 3 as the only factor of 342.
Since numbers divisible by 3 can be mistaken as only having 3 as a factor, remember that factors are numbers that can divide the given number equally. Other numbers that can divide 342 completely are 1, 2, 6, 19, 57, 114, 171, and 342.
Solved Examples for Factors of 342
Problem 1
Can you check whether 342 and 6 are co-prime?
No, 342 and 6 are not co-prime.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 342: 1, 2, 3, 6, 19, 38, 57, 114, 171, 342
Factors of 6: 1, 2, 3, 6
Here, the GCF is 6. So 342 and 6 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 342 is a multiple of 19
Yes, 342 is a multiple of 19
Explanation
Multiples of 19 are numbers we get when 19 is multiplied by another number.
19 × 18 = 342, so 342 is a multiple of 19.
Problem 3
Identify the factors of 342 that are perfect squares
The perfect square factors of 342 are 1 and 36.
Explanation
A perfect square is a number we get when the same number is multiplied twice.
The factors of 342 that satisfy this condition are 1 (1×1) and 36 (6×6).
Problem 4
Can 3 be used to divide 342?
Yes,3 can be used to divide 342 completely.
Explanation
The easy method to check is the number is divisible by 3, and the digits are to be summed up. 3 + 4 + 2 = 9. 9 is a multiple of 3.
So, 342 is divisible by 3.
Problem 5
Is 342 a prime number?
No, 342 is not a prime number.
Explanation
A prime number has only two factors: 1 and itself.
Since 342 has factors other than 1 and 342 (e.g., 2, 3, 6, 19, etc.), it is not a prime number.
FAQ’s for Factors of 342.
1.What are the factors of 342?
2.How do you determine if a number is a factor of 342?
3.What is the smallest factor of 342?
4.What is the largest factor of 342?
5.How many factors does 342 have?
6.How many odd factors does 342 have?
7.What factors go into 342?
8.Do any perfect squares exist in the factors of 342?
9.How can children in Singapore use numbers in everyday life to understand Factors of 342?
10.What are some fun ways kids in Singapore can practice Factors of 342 with numbers?
11.What role do numbers and Factors of 342 play in helping children in Singapore develop problem-solving skills?
12.How can families in Singapore create number-rich environments to improve Factors of 342 skills?
Glossaries for Factors of 342
Factors: Numbers that can divide a given number completely without leaving a remainder.
Prime Factors: Prime numbers that, when multiplied together, result in the given number.
Prime Factorization: The process of breaking down a number into its prime factors and expressing it in the form of a product.
Multiple: The result of multiplying a number by an integer.
Perfect Square: A number that is the product of a whole number multiplied by itself.
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About BrightChamps in Singapore
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.
