122 LearnersLast updated on May 26th, 2025
Factors of 773
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 773, how they are used in real life, and tips to learn them quickly.
What are the Factors of 773?
The numbers that divide 773 evenly are known as factors of 773.
A factor of 773 is a number that divides the number without a remainder.
The factors of 773 are 1, 7, 11, 49, 77, 773.
Negative factors of 773: -1, -7, -11, -49, -77, -773.
Prime factors of 773: 7 and 11.
Prime factorization of 773: 7 × 11 × 1.
The sum of factors of 773: 1 + 7 + 11 + 49 + 77 + 773 = 918
How to Find Factors of 773?
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 773. Identifying the numbers which are multiplied to get the number 773 is the multiplication method.
Step 1: Multiply 773 by 1, 773 × 1 = 773.
Step 2: Check for other numbers that give 773 after multiplying 7 × 11 × 1 = 77
Therefore, the positive factor pairs of 773 are: (1, 773), (7, 11, 1).
All these factor pairs result in 773.
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 773 by 1, 773 ÷ 1 = 773.
Step 2: Continue dividing 773 by the numbers until the remainder becomes 0.
773 ÷ 1 = 773
773 ÷ 7 = 110
428 (not a factor)
773 ÷ 11 = 70.272 (not a factor)
773 ÷ 49 = 15.775 (not a factor)
Therefore, the factors of 773 are: 1, 7, 11, 49, 77, 773.
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 773 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
773 ÷ 7 = 110.428 (not a whole number)
773 ÷ 11 = 70.272 (not a whole number)
Therefore, the prime factorization of 773 involves using the factors: 7 and 11.
The prime factorization of 773 is: 7 × 11 × 1.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. Here, the prime factors of 773 are found using 7 and 11. So, the prime factorization of 773 is: 7 × 11 × 1.
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 773: (1, 773).
Negative factor pairs of 773: (-1, -773).
Common Mistakes and How to Avoid Them in Factors of 773
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 word. Always remember to include 1 and the number itself.
For example, in factors of 773, 1 and 773 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 773 consist of -1, -7, -11, 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 773/1.5 = 515.333, 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 773 are prime numbers.
For example, 7 and 11 are the prime factors of 773, but it has other factors like 49, 77.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 773 as 7 × 11 × 1 and missing all the key factors.
Factors of 773 Examples
Problem 1
There are 7 teams and 773 points. How will they divide it equally?
Each team will get approximately 110.428 points, which indicates an unequal division.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
773/7 = 110.428
Problem 2
A rectangular plot has a length of 11 meters and a total area of 773 square meters. Find the width?
70.272 meters, which indicates an error as it should be a whole number.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
773 = 11 × width
To find the value of width,
773/11 = width
Width = 70.272.
Problem 3
A concert has 49 rows and 773 seats. How many seats will be in each row if they are distributed equally?
Approximately 15.775 seats, indicating an unequal distribution.
Explanation
To find the seats in each row, divide the total seats by the rows.
773/49 = 15.775
Problem 4
A charity has 773 gifts and wants to divide them into 11 different categories. How many gifts will each category receive?
Approximately 70.272 gifts per category, indicating unequal distribution.
Explanation
Dividing the gifts into categories, we will get the number of gifts in each category.
773/11 = 70.272
Problem 5
A library has 773 books to arrange on 7 shelves. How many books will go on each shelf if distributed equally?
Each shelf will have approximately 110.428 books, indicating an unequal distribution.
Explanation
Divide total books by shelves.
773/7 = 110.428
FAQs on Factors of 773
1.What are the factors of 773?
2.Mention the prime factors of 773.
3.Is 773 a multiple of 7?
4.Mention the factor pairs of 773?
5.What is the square of 773?
Important Glossaries for Factors of 773
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 773 are 1, 7, 11, 49, 77, and 773.
- Prime factors: The factors which are prime numbers. For example, 7 and 11 are prime factors of 773.
- 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 773 is (1, 773).
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 773 is 7 × 11 × 1.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, for 773, this involves using its prime factors 7 and 11.
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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.
