120 LearnersLast updated on May 26th, 2025
Factors of 788
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 788, how they are used in real life, and tips to learn them quickly.
What are the Factors of 788?
The numbers that divide 788 evenly are known as factors of 788.
A factor of 788 is a number that divides the number without remainder.
The factors of 788 are 1, 2, 4, 197, 394, and 788.
Negative factors of 788: -1, -2, -4, -197, -394, and -788.
Prime factors of 788: 2 and 197.
Prime factorization of 788: 2² × 197.
The sum of factors of 788: 1 + 2 + 4 + 197 + 394 + 788 = 1386
How to Find Factors of 788?
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 788. Identifying the numbers which are multiplied to get the number 788 is the multiplication method.
Step 1: Multiply 788 by 1, 788 × 1 = 788.
Step 2: Check for other numbers that give 788 after multiplying
2 × 394 = 788
4 × 197 = 788
Therefore, the positive factor pairs of 788 are: (1, 788), (2, 394), and (4, 197).
All these factor pairs result in 788. 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 the simple division method:
Step 1: Divide 788 by 1, 788 ÷ 1 = 788.
Step 2: Continue dividing 788 by the numbers until the remainder becomes 0.
788 ÷ 1 = 788
788 ÷ 2 = 394
788 ÷ 4 = 197
Therefore, the factors of 788 are: 1, 2, 4, 197, 394, 788.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 788 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
788 ÷ 2 = 394
394 ÷ 2 = 197
197 ÷ 197 = 1
The prime factors of 788 are 2 and 197.
The prime factorization of 788 is 2² × 197.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 788 is divided by 2 to get 394.
Step 2: Now divide 394 by 2 to get 197. Here, 197 is a prime number that cannot be divided anymore. So, the prime factorization of 788 is 2² × 197.
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 788: (1, 788), (2, 394), (4, 197).
Negative factor pairs of 788: (-1, -788), (-2, -394), (-4, -197).
Common Mistakes and How to Avoid Them in Factors of 788
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
Students 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 788, 1 and 788 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 788 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Students might sometimes add fractions as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor because 788/1.5 = 525.333, 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 788 are prime numbers. For example, 2 and 197 are the prime factors of 788, but it has other factors like 4, 394.
Mistake 5
Mistake in Factorization
Students might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 788 as 2² × 197 and missing all the key factors.
Factors of 788 Examples
Problem 1
A bakery has 788 cupcakes and 4 display trays. How many cupcakes will be on each tray?
Each tray will have 197 cupcakes.
Explanation
To divide the cupcakes equally, we need to divide the total cupcakes by the number of trays.
788/4 = 197
Problem 2
A garden has a rectangular shape with a length of 394 meters and a total area of 788 square meters. Find the width.
2 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
788 = 394 × width
To find the value of width, we need to shift 394 to the left side.
788/394 = width
Width = 2.
Problem 3
There are 2 teams and 788 players. How many players will be in each team?
Each team will have 394 players.
Explanation
To find the players in each team, divide the total players by the teams.
788/2 = 394
Problem 4
A library has 788 books, and 197 shelves. How many books are there on each shelf?
There are 4 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
788/197 = 4
Problem 5
788 apples need to be packed into 2 boxes. How many apples will go in each box?
Each box will have 394 apples.
Explanation
Divide total apples by boxes.
788/2 = 394
FAQs on Factors of 788
1.What are the factors of 788?
2.Mention the prime factors of 788.
3.Is 788 a multiple of 4?
4.Mention the factor pairs of 788?
5.What is the square of 788?
Important Glossaries for Factor of 788
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 788 are 1, 2, 4, 197, 394, and 788.
- Prime factors: The factors which are prime numbers. For example, 2 and 197 are prime factors of 788.
- 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 788 are (1, 788), (2, 394), etc.
- Prime factorization: Breaking down a number into its prime components. For example, the prime factorization of 788 is 2² × 197.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 788 is a multiple of 4.
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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.
