120 LearnersLast updated on May 26th, 2025
Factors of 774
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 774, how they are used in real life, and tips to learn them quickly.
What are the Factors of 774?
The numbers that divide 774 evenly are known as factors of 774. A factor of 774 is a number that divides the number without remainder.
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774.
Negative factors of 774: -1, -2, -3, -6, -9, -18, -43, -86, -129, -258, -387, and -774.
Prime factors of 774: 2, 3, and 43.
Prime factorization of 774: 2 × 3 × 3 × 43.
The sum of factors of 774: 1 + 2 + 3 + 6 + 9 + 18 + 43 + 86 + 129 + 258 + 387 + 774 = 1716
How to Find Factors of 774?
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 774. Identifying the numbers which are multiplied to get the number 774 is the multiplication method.
Step 1: Multiply 774 by 1, 774 × 1 = 774.
Step 2: Check for other numbers that give 774 after multiplying
2 × 387 = 774
3 × 258 = 774
6 × 129 = 774
9 × 86 = 774
18 × 43 = 774
Therefore, the positive factor pairs of 774 are: (1, 774), (2, 387), (3, 258), (6, 129), (9, 86), (18, 43).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 simple division method
Step 1: Divide 774 by 1, 774 ÷ 1 = 774.
Step 2: Continue dividing 774 by the numbers until the remainder becomes 0.
774 ÷ 1 = 774
774 ÷ 2 = 387
774 ÷ 3 = 258
774 ÷ 6 = 129
774 ÷ 9 = 86
774 ÷ 18 = 43
Therefore, the factors of 774 are: 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774.
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 774 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
774 ÷ 2 = 387
387 ÷ 3 = 129
129 ÷ 3 = 43
43 ÷ 43 = 1
The prime factors of 774 are 2, 3, and 43.
The prime factorization of 774 is: 2 × 3 × 3 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 774 is divided by 2 to get 387.
Step 2: Now divide 387 by 3 to get 129.
Step 3: Then divide 129 by 3 to get 43. Here, 43 is a prime number and cannot be divided further. So, the prime factorization of 774 is: 2 × 3 × 3 × 43.
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 774: (1, 774), (2, 387), (3, 258), (6, 129), (9, 86), and (18, 43).
Negative factor pairs of 774: (-1, -774), (-2, -387), (-3, -258), (-6, -129), (-9, -86), and (-18, -43).
Common Mistakes and How to Avoid Them in Factors of 774
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 774, 1 and 774 are also factors.
Mistake 2
Missing Negative Factors
We often mention positive factors only. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 774 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 774/1.5 = 516, 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 774 are prime numbers.
For example, 2, 3, and 43 are the prime factors of 774, but it has other factors like 6, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 774 as 2 × 3 × 3 × 43 and missing all the key factors.
Factors of 774 Examples
Problem 1
There are 9 soccer teams and 774 fans. How will they distribute the fans equally among the teams?
Each team will have 86 fans.
Explanation
To divide the fans equally, we need to divide the total fans by the number of teams.
774/9 = 86
Problem 2
A rectangular park has a length of 18 meters and a total area of 774 square meters. Find the width.
43 meters.
Explanation
To find the width of the park, we use the formula,
Area = length × width
774 = 18 × width
To find the value of width, we need to shift 18 to the left side.
774/18 = width
Width = 43.
Problem 3
There are 3 trucks and 774 boxes. How many boxes will be in each truck?
Each truck will have 258 boxes.
Explanation
To find the boxes in each truck, divide the total boxes by the number of trucks.
774/3 = 258
Problem 4
In a conference, there are 774 participants and 6 rooms. How many participants are there in each room?
There are 129 participants in each room.
Explanation
Dividing the participants by the total rooms, we will get the number of participants in each room.
774/6 = 129
Problem 5
774 books need to be arranged in 2 libraries. How many books will go in each library?
Each library will have 387 books.
Explanation
Divide total books by the libraries.
774/2 = 387
FAQs on Factors of 774
1.What are the factors of 774?
2.Mention the prime factors of 774.
3.Is 774 a multiple of 3?
4.Mention the factor pairs of 774.
5.What is the square of 774?
Important Glossaries for Factors of 774
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 43 are prime factors of 774.
- 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 774 are (1, 774), (2, 387), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 774 is 2 × 3 × 3 × 43.
- Multiple: A number that can be divided by another number without a remainder. For example, 774 is a multiple of 3.
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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.
