116 LearnersLast updated on May 26th, 2025
Factors of 771
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, arranging things, etc. In this topic, we will learn about the factors of 771, how they are used in real life, and tips to learn them quickly.
What are the Factors of 771?
The numbers that divide 771 evenly are known as factors of 771.
A factor of 771 is a number that divides the number without a remainder.
The factors of 771 are 1, 3, 257, and 771.
Negative factors of 771: -1, -3, -257, and -771.
Prime factors of 771: 3 and 257.
Prime factorization of 771: 3 × 257.
The sum of factors of 771: 1 + 3 + 257 + 771 = 1032
How to Find Factors of 771?
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 771. Identifying the numbers which are multiplied to get the number 771 is the multiplication method.
Step 1: Multiply 771 by 1, 771 × 1 = 771.
Step 2: Check for other numbers that give 771 after multiplying 3 × 257 = 771
Therefore, the positive factor pairs of 771 are: (1, 771) and (3, 257). All these factor pairs result in 771.
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 771 by 1, 771 ÷ 1 = 771.
Step 2: Continue dividing 771 by the numbers until the remainder becomes 0.
771 ÷ 1 = 771
771 ÷ 3 = 257
Therefore, the factors of 771 are: 1, 3, 257, 771.
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 771 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
771 ÷ 3 = 257
257 is a prime number and cannot be divided further.
The prime factors of 771 are 3 and 257.
The prime factorization of 771 is: 3 × 257.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 771 is divided by 3 to get 257.
Here, 257 is a prime number and cannot be divided anymore.
So, the prime factorization of 771 is: 3 × 257.
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 771: (1, 771) and (3, 257).
Negative factor pairs of 771: (-1, -771) and (-3, -257).
Common Mistakes and How to Avoid Them in Factors of 771
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 771, 1 and 771 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 771 consist of -1, -3, 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 771/1.5 = 514, 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 771 are prime numbers.
For example, 3 and 257 are the prime factors of 771, but it has other factors like 1, 771.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not recognizing 3 × 257 as the correct factorization for 771 and missing key factors.
Factors of 771 Examples
Problem 1
There are 3 friends and 771 marbles. How will they divide it equally?
They will get 257 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of friends.
771/3 = 257
Problem 2
A parking area is rectangular, the length of the area is 3 meters and the total area is 771 square meters. Find the width?
257 meters.
Explanation
To find the width of the area, we use the formula,
Area = length × width
771 = 3 × width
To find the value of width, we need to shift 3 to the left side.
771/3 = width
Width = 257.
Problem 3
There are 257 gift bags and 771 candies. How many candies will be in each bag?
Each bag will have 3 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
771/257 = 3
Problem 4
In a class, there are 771 students, and 3 groups. How many students are there in each group?
There are 257 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
771/3 = 257
Problem 5
771 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 257 books.
Explanation
Divide total books with shelves.
771/3 = 257
FAQs on Factors of 771
1.What are the factors of 771?
2.Mention the prime factors of 771.
3.Is 771, a multiple of 3?
4.Mention the factor pairs of 771?
5.What is the square of 771?
Important Glossaries for Factors of 771
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 771 are 1, 3, 257, and 771.
- Prime factors: The factors which are prime numbers. For example, 3 and 257 are prime factors of 771.
- 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 771 are (1, 771) and (3, 257).
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 771 is 3 × 257.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 771 is a multiple of 3.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 771
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.
