117 LearnersLast updated on May 26th, 2025
Factors of 698
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 698, how they are used in real life, and tips to learn them quickly.
What are the Factors of 698?
The numbers that divide 698 evenly are known as factors of 698.
A factor of 698 is a number that divides the number without remainder.
The factors of 698 are 1, 2, 349, and 698.
Negative factors of 698: -1, -2, -349, and -698.
Prime factors of 698: 2 and 349.
Prime factorization of 698: 2 × 349.
The sum of factors of 698: 1 + 2 + 349 + 698 = 1050
How to Find Factors of 698?
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 698. Identifying the numbers which are multiplied to get the number 698 is the multiplication method.
Step 1: Multiply 698 by 1, 698 × 1 = 698.
Step 2: Check for other numbers that give 698 after multiplying 2 × 349 = 698
Therefore, the positive factor pairs of 698 are: (1, 698), (2, 349). All these factor pairs result in 698.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 698 by 1, 698 ÷ 1 = 698.
Step 2: Continue dividing 698 by the numbers until the remainder becomes 0.
698 ÷ 1 = 698
698 ÷ 2 = 349
Therefore, the factors of 698 are: 1, 2, 349, and 698.
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 698 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
698 ÷ 2 = 349
349 is already a prime number.
The prime factors of 698 are 2 and 349.
The prime factorization of 698 is: 2 × 349.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 698 is divided by 2 to get 349. Here, 349 is a prime number, and it cannot be divided further. So, the prime factorization of 698 is: 2 × 349.
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 698: (1, 698), (2, 349).
Negative factor pairs of 698: (-1, -698), (-2, -349).
Common Mistakes and How to Avoid Them in Factors of 698
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 698, 1 and 698 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 698 consist of -1, -2, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 698/1.5 = 465.333, 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 698 are prime numbers.
For example, 2 and 349 are the prime factors of 698, but it has other factors like 1 and 698.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 698 as 2 × 349 and missing all the key factors.
Factors of 698 Examples
Problem 1
There are 2 teams and 698 students. How will they divide equally?
They will get 349 students each.
Explanation
To divide the students equally, we need to divide the total students by the number of teams.
698/2 = 349
Problem 2
A garden is rectangular, the width of the garden is 2 meters and the total area is 698 square meters. Find the length?
349 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
698 = length × 2
To find the value of length, we need to shift 2 to the left side.
698/2 = length
Length = 349.
Problem 3
There are 349 boxes and 698 cookies. How many cookies will be in each box?
Each box will have 2 cookies.
Explanation
To find the cookies in each box, divide the total cookies by the boxes.
698/349 = 2
Problem 4
In a school, there are 698 students, and 349 classes. How many students are there in each class?
There are 2 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
698/349 = 2
Problem 5
698 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 349 books.
Explanation
Divide total books by shelves.
698/2 = 349
FAQs on Factors of 698
1.What are the factors of 698?
2.Mention the prime factors of 698.
3.Is 698 a multiple of 349?
4.Mention the factor pairs of 698?
5.What is the square of 698?
6.How can children in Qatar use numbers in everyday life to understand Factors of 698?
7.What are some fun ways kids in Qatar can practice Factors of 698 with numbers?
8.What role do numbers and Factors of 698 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 698 skills?
Important Glossaries for Factor of 698
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 698 are 1, 2, 349, and 698.
- Prime factors: The factors which are prime numbers. For example, 2 and 349 are prime factors of 698.
- 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 698 are (1, 698) and (2, 349).
- Prime factorization: Breaking down a number into its prime number components. For example, 698 = 2 × 349.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 698 is a multiple of 2 and 349.
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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.
