118 LearnersLast updated on May 26th, 2025
Factors of 351
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 351, how they are used in real life, and tips to learn them quickly.
What are the Factors of 351?
The numbers that divide 351 evenly are known as factors of 351.
A factor of 351 is a number that divides the number without remainder.
The factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351.
Negative factors of 351: -1, -3, -9, -13, -27, -39, -117, and -351.
Prime factors of 351: 3 and 13.
Prime factorization of 351: 3² × 13.
The sum of factors of 351: 1 + 3 + 9 + 13 + 27 + 39 + 117 + 351 = 560
How to Find Factors of 351?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 351. Identifying the numbers which are multiplied to get the number 351 is the multiplication method.
Step 1: Multiply 351 by 1, 351 × 1 = 351.
Step 2: Check for other numbers that give 351 after multiplying
3 × 117 = 351
9 × 39 = 351
13 × 27 = 351
Therefore, the positive factor pairs of 351 are: (1, 351), (3, 117), (9, 39), (13, 27).
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 351 by 1, 351 ÷ 1 = 351.
Step 2: Continue dividing 351 by the numbers until the remainder becomes 0.
351 ÷ 1 = 351
351 ÷ 3 = 117
351 ÷ 9 = 39
351 ÷ 13 = 27
Therefore, the factors of 351 are: 1, 3, 9, 13, 27, 39, 117, and 351.
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 351 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
351 ÷ 3 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 351 are 3 and 13.
The prime factorization of 351 is: 3² × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 351 is divided by 3 to get 117.
Step 2: Now divide 117 by 3 to get 39.
Step 3: Then divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 351 is: 3² × 13.
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 351: (1, 351), (3, 117), (9, 39), and (13, 27).
Negative factor pairs of 351: (-1, -351), (-3, -117), (-9, -39), and (-13, -27).
Common Mistakes and How to Avoid Them in Factors of 351
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 351, 1 and 351 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 351 include -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 351/1.5 = 234, 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 351 are prime numbers.
For example, 3 and 13 are the prime factors of 351, but it has other factors like 9, 39.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 351 as 3² × 13 and missing all the key factors.
Factors of 351 Examples
Problem 1
There are 13 teams and 351 participants. How will they divide the participants equally?
They will get 27 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
351/13 = 27
Problem 2
A garden is rectangular, the length of the garden is 9 meters and the total area is 351 square meters. Find the width.
39 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
351 = 9 × width
To find the value of width, we need to shift 9 to the left side.
351/9 = width
Width = 39.
Problem 3
There are 39 boxes and 351 items. How many items will be in each box?
Each box will have 9 items.
Explanation
To find the items in each box, divide the total items by the boxes.
351/39 = 9
Problem 4
In a class, there are 351 students, and 3 groups. How many students are there in each group?
There are 117 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
351/3 = 117
Problem 5
351 books need to be arranged in 13 shelves. How many books will go on each shelf?
Each of the shelves has 27 books.
Explanation
Divide total books by shelves.
351/13 = 27
FAQs on Factors of 351
1.What are the factors of 351?
2.Mention the prime factors of 351.
3.Is 351 a multiple of 9?
4.Mention the factor pairs of 351?
5.What is the square of 351?
6.How can children in Thailand use numbers in everyday life to understand Factors of 351?
7.What are some fun ways kids in Thailand can practice Factors of 351 with numbers?
8.What role do numbers and Factors of 351 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 351 skills?
Important Glossaries for Factor of 351
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351.
- Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 351.
- 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 351 are (1, 351), (3, 117), etc.
- Prime factorization: Breaking down a number into a product of its prime factors. For example, the prime factorization of 351 is 3² × 13.
- Multiple: A number that can be divided by another number without a remainder. For example, 351 is a multiple of 9.
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About BrightChamps in Thailand
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.
