121 LearnersLast updated on May 26th, 2025
Factors of 349
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 349, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 349?
The numbers that divide 349 evenly are known as factors of 349.
A factor of 349 is a number that divides the number without remainder.
The factors of 349 are 1 and 349.
Negative factors of 349: -1 and -349.
Prime factors of 349: 349 (since 349 is a prime number).
Prime factorization of 349: 3491.
The sum of factors of 349: 1 + 349 = 350
How to Find Factors of 349?
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 349.
Since 349 is a prime number, the only multiplication that works is:
Step 1: Multiply 349 by 1, 349 × 1 = 349.
Therefore, the positive factor pair of 349 is: (1, 349).
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 a simple division method:
Step 1: Divide 349 by 1, 349 ÷ 1 = 349.
Step 2: Continue attempting to divide 349 by numbers up to its square root (approx. 18.68).
Since no divisions result in a whole number other than dividing by 1 and 349 itself, we conclude:
The factors of 349 are: 1 and 349.
Prime Factors and Prime Factorization
The factors can be found by dividing the number by prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, we attempt to divide 349 by prime numbers.
Since 349 itself is a prime number, it cannot be factored further.
The prime factors of 349 are 349. The prime factorization of 349 is: 3491.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. For 349, since it's a prime number, the factor tree is simple:
Step 1: Recognize that 349 is a prime number. So, the prime factorization of 349 is: 3491.
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 pair of 349: (1, 349).
Negative factor pair of 349: (-1, -349).
Common Mistakes and How to Avoid Them in Factors of 349
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 349, 1 and 349 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 349 consist of -1 and -349.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 349/1.5 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 349 must be prime numbers. For instance, 349 is a prime factor of itself, but it has another factor, 1.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not recognizing that 349 is 3491 as a prime factorization.
Factors of 349 Examples
Problem 1
There are 349 pages in a book. If each page weighs the same, how many pages would weigh the same as the entire book?
349 pages.
Explanation
Each page is an equal unit of the book, so the entire book is made up of 349 pages, which means all pages together weigh the same as the book itself.
Problem 2
A ribbon is 349 cm long. If you cut it into pieces each 1 cm long, how many pieces will you have?
349 pieces.
Explanation
To find the number of pieces, divide the total length by the length of each piece.
349/1 = 349
Problem 3
A flagpole is 349 cm tall. If each section is 349 cm, how many sections does it consist of?
1 section.
Explanation
The entire flagpole is one section since its total height is 349 cm, which is the height of the section itself.
349/349 = 1
Problem 4
A library has 349 identical books. If you want to arrange them equally in 1 row, how many books will be in the row?
349 books.
Explanation
To arrange the books equally in one row, you would simply have all 349 books in that single row.
349/1 = 349
Problem 5
A company has 349 employees and wants to give each employee a personalized item. How many items are needed?
349 items.
Explanation
To give each employee one item, the company needs as many items as there are employees.
349/1 = 349
FAQs on Factors of 349
1.What are the factors of 349?
2.Mention the prime factors of 349.
3.Is 349 a multiple of any number other than 1 and itself?
4.Mention the factor pair of 349?
5.What is the square of 349?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 349?
7.What are some fun ways kids in Vietnam can practice Factors of 349 with numbers?
8.What role do numbers and Factors of 349 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 349 skills?
Important Glossaries for Factors of 349
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 349 are 1 and 349.
- Prime factors: The factors that are prime numbers. For example, 349 is a prime factor of itself.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 349 is (1, 349).
- Prime number: A number that has no divisors other than 1 and itself. For example, 349 is a prime number.
- Factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 349 is 349^1.
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About BrightChamps in Vietnam
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.
