118 LearnersLast updated on May 26th, 2025
Factors of 775
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 775, how they are used in real life, and tips to learn them quickly.
What are the Factors of 775?
The numbers that divide 775 evenly are known as factors of 775.
A factor of 775 is a number that divides the number without a remainder.
The factors of 775 are 1, 5, 25, 31, 155, and 775.
Negative factors of 775: -1, -5, -25, -31, -155, and -775.
Prime factors of 775: 5 and 31.
Prime factorization of 775: 5 × 31 × 5.
The sum of factors of 775: 1 + 5 + 25 + 31 + 155 + 775 = 992
How to Find Factors of 775?
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 775. Identifying the numbers which are multiplied to get the number 775 is the multiplication method.
Step 1: Multiply 775 by 1, 775 × 1 = 775.
Step 2: Check for other numbers that give 775 after multiplying: 5 × 155 = 775 25 × 31 = 775
Therefore, the positive factor pairs of 775 are: (1, 775), (5, 155), and (25, 31).
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 a simple division method:
Step 1: Divide 775 by 1, 775 ÷ 1 = 775.
Step 2: Continue dividing 775 by the numbers until the remainder becomes 0.
775 ÷ 1 = 775
775 ÷ 5 = 155
775 ÷ 25 = 31
Therefore, the factors of 775 are: 1, 5, 25, 31, 155, and 775.
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 775 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
775 ÷ 5 = 155
155 ÷ 5 = 31
31 ÷ 31 = 1
The prime factors of 775 are 5 and 31.
The prime factorization of 775 is: 5 × 5 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 775 is divided by 5 to get 155.
Step 2: Now divide 155 by 5 to get 31.
Step 3: Here, 31 is a prime number that cannot be divided anymore. So, the prime factorization of 775 is: 5 × 5 × 31.
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 775: (1, 775), (5, 155), and (25, 31).
Negative factor pairs of 775: (-1, -775), (-5, -155), and (-25, -31).
Common Mistakes and How to Avoid Them in Factors of 775
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 775, 1 and 775 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 775 include -1, -5, -25, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 775/1.5 ≈ 516.67 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 775 are prime numbers.
For example, 5 and 31 are the prime factors of 775, but it has other factors like 25.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing the wrong factors.
For example, not breaking 775 as 5 × 5 × 31 and missing all the key factors.
Factors of 775 Examples
Problem 1
A farmer has 775 apples and wants to pack them into crates, with each crate holding 5 apples. How many crates does he need?
He will need 155 crates.
Explanation
To pack the apples equally, we need to divide the total apples by the number of apples per crate.
775/5 = 155
Problem 2
A rectangular garden has a length of 25 meters, and the total area is 775 square meters. Find the width.
31 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
775 = 25 × width
To find the value of width, we need to shift 25 to the left side.
775/25 = width
Width = 31.
Problem 3
There are 31 rooms in a hotel and 775 guests. How many guests will be in each room if they are distributed equally?
Each room will have 25 guests.
Explanation
To find the guests in each room, divide the total guests by the number of rooms.
775/31 = 25
Problem 4
A teacher has 775 worksheets to distribute among 5 classes. How many worksheets will each class receive?
Each class will receive 155 worksheets.
Explanation
Dividing the worksheets by the total number of classes, we will get the number of worksheets per class.
775/5 = 155
Problem 5
A library has 775 books to be placed on 25 shelves. How many books will go on each shelf?
Each shelf will have 31 books.
Explanation
Divide total books by shelves.
775/25 = 31
FAQs on Factors of 775
1.What are the factors of 775?
2.Mention the prime factors of 775.
3.Is 775 a multiple of 31?
4.Mention the factor pairs of 775?
5.What is the square of 775?
Important Glossaries for Factors of 775
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 775 are 1, 5, 25, 31, 155, and 775.
- Prime factors: The factors which are prime numbers. For example, 5 and 31 are prime factors of 775.
- 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 775 are (1, 775), (5, 155), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 775 is 5 × 5 × 31.
- Negative factors: Factors that are negative integers. For example, -1, -5, -25, -31, -155, and -775 are negative factors of 775.
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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.
