101 LearnersLast updated on May 26th, 2025
Factors of 693
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally or arranging things. In this topic, we will learn about the factors of 693, how they are used in real life, and tips to learn them quickly.
What are the Factors of 693?
The numbers that divide 693 evenly are known as factors of 693.
A factor of 693 is a number that divides the number without leaving a remainder.
The factors of 693 are 1, 3, 7, 9, 21, 33, 77, 99, 231, and 693.
Negative factors of 693: -1, -3, -7, -9, -21, -33, -77, -99, -231, and -693.
Prime factors of 693: 3, 7, and 11.
Prime factorization of 693: 3 × 3 × 7 × 11.
The sum of factors of 693: 1 + 3 + 7 + 9 + 21 + 33 + 77 + 99 + 231 + 693 = 1174
How to Find Factors of 693?
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 693. Identifying the numbers which are multiplied to get the number 693 is the multiplication method.
Step 1: Multiply 693 by 1, 693 × 1 = 693.
Step 2: Check for other numbers that give 693 after multiplying:
3 × 231 = 693
7 × 99 = 693
9 × 77 = 693
21 × 33 = 693
Therefore, the positive factor pairs of 693 are: (1, 693), (3, 231), (7, 99), (9, 77), (21, 33).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Divide the given number with whole numbers until the remainder becomes zero and list out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 693 by 1, 693 ÷ 1 = 693.
Step 2: Continue dividing 693 by the numbers until the remainder becomes 0.
693 ÷ 1 = 693
693 ÷ 3 = 231
693 ÷ 7 = 99
693 ÷ 9 = 77
693 ÷ 21 = 33
Therefore, the factors of 693 are: 1, 3, 7, 9, 21, 33, 77, 99, 231, 693.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 693 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
693 ÷ 3 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 693 are 3, 7, and 11.
The prime factorization of 693 is: 3 × 3 × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 693 is divided by 3 to get 231.
Step 2: Now divide 231 by 3 to get 77.
Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 693 is: 3 × 3 × 7 × 11.
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 693: (1, 693), (3, 231), (7, 99), (9, 77), and (21, 33).
Negative factor pairs of 693: (-1, -693), (-3, -231), (-7, -99), (-9, -77), and (-21, -33).
Common Mistakes and How to Avoid Them in Factors of 693
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 693, 1 and 693 are also factors.
Factors of 693 Examples
Problem 1
There are 9 students and 693 candies. How will they distribute them equally?
They will get 77 candies each.
Explanation
To distribute the candies equally, divide the total candies by the number of students.
693/9 = 77
Problem 2
A garden is rectangular, the length of the garden is 21 meters and the total area is 693 square meters. Find the width.
33 meters.
Explanation
To find the width of the garden, use the formula:
Area = length × width
693 = 21 × width
To find the value of width, shift 21 to the left side.
693/21 = width
Width = 33.
Problem 3
There are 77 boxes and 693 apples. How many apples will be in each box?
Each box will have 9 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
693/77 = 9
Problem 4
In a hall, there are 693 chairs, and 11 rows. How many chairs are there in each row?
There are 63 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
693/11 = 63
Problem 5
693 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each shelf will have 231 books.
Explanation
Divide total books by shelves.
693/3 = 231
FAQs on Factors of 693
1.What are the factors of 693?
2.Mention the prime factors of 693.
3.Is 693 a multiple of 7?
4.Mention the factor pairs of 693?
5.What is the square of 693?
Important Glossaries for Factors of 693
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 693 are 1, 3, 7, 9, 21, 33, 77, 99, 231, and 693.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 11 are prime factors of 693.
- 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 693 are (1, 693), (3, 231), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 693 is 3 × 3 × 7 × 11.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to a given number. For example, 3 and 231 are a multiplication pair for 693.
Explore More numbers
Previous to Factors of 693
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.
