118 LearnersLast updated on May 26th, 2025
Factors of 354
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 354, how they are used in real life, and tips to learn them quickly.
What are the Factors of 354?
The numbers that divide 354 evenly are known as factors of 354.
A factor of 354 is a number that divides the number without remainder.
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354.
Negative factors of 354: -1, -2, -3, -6, -59, -118, -177, and -354. Prime factors of 354: 2, 3, and 59.
Prime factorization of 354: 2 × 3 × 59.
The sum of factors of 354: 1 + 2 + 3 + 6 + 59 + 118 + 177 + 354 = 720
How to Find Factors of 354?
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 354. Identifying the numbers which are multiplied to get the number 354 is the multiplication method.
Step 1: Multiply 354 by 1, 354 × 1 = 354.
Step 2: Check for other numbers that give 354 after multiplying 2 × 177 = 354 3 × 118 = 354 6 × 59 = 354
Therefore, the positive factor pairs of 354 are: (1, 354), (2, 177), (3, 118), (6, 59).
All these factor pairs result in 354.
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 354 by 1, 354 ÷ 1 = 354.
Step 2: Continue dividing 354 by the numbers until the remainder becomes 0.
354 ÷ 1 = 354
354 ÷ 2 = 177
354 ÷ 3 = 118
354 ÷ 6 = 59
Therefore, the factors of 354 are: 1, 2, 3, 6, 59, 118, 177, 354.
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 354 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
354 ÷ 2 = 177
177 ÷ 3 = 59
59 ÷ 59 = 1
The prime factors of 354 are 2, 3, and 59.
The prime factorization of 354 is: 2 × 3 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 354 is divided by 2 to get 177.
Step 2: Now divide 177 by 3 to get 59.
Step 3: Divide 59 by 59 to get 1. Here, 59 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 354 is: 2 × 3 × 59.
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 354: (1, 354), (2, 177), (3, 118), and (6, 59).
Negative factor pairs of 354: (-1, -354), (-2, -177), (-3, -118), and (-6, -59).
Common Mistakes and How to Avoid Them in Factors of 354
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 354, 1 and 354 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 354 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 354/1.5 = 236, 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 354 are prime numbers.
For example, 2, 3, and 59 are the prime factors of 354, but it has other factors like 6, 177.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 354 as 2 × 3 × 59 and missing all the key factors.
Factors of 354 Examples
Problem 1
There are 6 teams and 354 players. How will they divide them equally?
They will get 59 players each.
Explanation
To divide the players equally, we need to divide the total players with the number of teams.
354/6 = 59
Problem 2
A garden is rectangular, the length of the garden is 59 meters, and the total area is 354 square meters. Find the width?
6 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
354 = 59 × width
To find the value of width, we need to shift 59 to the left side.
354/59 = width
Width = 6.
Problem 3
There are 3 boxes and 354 candies. How many candies will be in each box?
Each box will have 118 candies.
Explanation
To find the candies in each box, divide the total candies with the boxes.
354/3 = 118
Problem 4
In a class, there are 354 students, and 2 sections. How many students are there in each section?
There are 177 students in each section.
Explanation
Dividing the students with the total sections, we will get the number of students in each section.
354/2 = 177
Problem 5
354 plants need to be arranged in 59 rows. How many plants will go in each row?
Each of the rows has 6 plants.
Explanation
Divide total plants with rows.
354/59 = 6
FAQs on Factors of 354
1.What are the factors of 354?
2.Mention the prime factors of 354.
3.Is 354 a multiple of 3?
4.Mention the factor pairs of 354?
5.What is the square of 354?
6.How can children in United States use numbers in everyday life to understand Factors of 354?
7.What are some fun ways kids in United States can practice Factors of 354 with numbers?
8.What role do numbers and Factors of 354 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 354 skills?
Important Glossaries for Factor of 354
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 59 are prime factors of 354.
- 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 354 are (1, 354), (2, 177), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 354 is 2 × 3 × 59.
- Multiple: A number that can be divided by another number without a remainder. For example, 354 is a multiple of 3.
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About BrightChamps in United States
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.
