119 LearnersLast updated on May 26th, 2025
Factors of 772
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 772, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 772?
The numbers that divide 772 evenly are known as factors of 772.
A factor of 772 is a number that divides the number without remainder.
The factors of 772 are 1, 2, 4, 193, 386, and 772.
Negative factors of 772: -1, -2, -4, -193, -386, and -772.
Prime factors of 772: 2 and 193.
Prime factorization of 772: 2² × 193.
The sum of factors of 772: 1 + 2 + 4 + 193 + 386 + 772 = 1358
How to Find Factors of 772?
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 772. Identifying the numbers which are multiplied to get the number 772 is the multiplication method.
Step 1: Multiply 772 by 1, 772 × 1 = 772.
Step 2: Check for other numbers that give 772 after multiplying
2 × 386 = 772
4 × 193 = 772
Therefore, the positive factor pairs of 772 are: (1, 772), (2, 386), and (4, 193). All these factor pairs result in 772.
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 a whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 772 by 1, 772 ÷ 1 = 772.
Step 2: Continue dividing 772 by the numbers until the remainder becomes 0.
772 ÷ 1 = 772
772 ÷ 2 = 386
772 ÷ 4 = 193
Therefore, the factors of 772 are: 1, 2, 4, 193, 386, 772.
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 772 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
772 ÷ 2 = 386
386 ÷ 2 = 193
193 is a prime number and cannot be divided further.
The prime factors of 772 are 2 and 193.
The prime factorization of 772 is: 2² × 193.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 772 is divided by 2 to get 386.
Step 2: Now divide 386 by 2 to get 193. Here, 193 is a prime number and cannot be divided further.
So, the prime factorization of 772 is: 2² × 193.
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 772: (1, 772), (2, 386), and (4, 193).
Negative factor pairs of 772: (-1, -772), (-2, -386), and (-4, -193).
Common Mistakes and How to Avoid Them in Factors of 772
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 772, 1 and 772 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 772 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 772/1.5 = 514.666, 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 772 are prime numbers.
For example, 2 and 193 are the prime factors of 772, but it has other factors like 4, 386.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 772 as 2² × 193 and missing all the key factors.
Factors of 772 Examples
Problem 1
There are 2 teams and 772 tickets. How will they divide them equally?
They will get 386 tickets each.
Explanation
To divide the tickets equally, we need to divide the total tickets by the number of teams.
772/2 = 386
Problem 2
A rectangular garden has a length of 4 meters and a total area of 772 square meters. Find the width.
193 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
772 = 4 × width
To find the value of width, we need to shift 4 to the left side.
772/4 = width
Width = 193.
Problem 3
There are 4 containers and 772 liters of oil. How many liters of oil will be in each container?
Each container will have 193 liters of oil.
Explanation
To find the oil in each container, divide the total oil by the containers.
772/4 = 193
Problem 4
In a school, there are 772 students and 193 classes. How many students are there in each class?
There are 4 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
772/193 = 4
Problem 5
772 plants need to be arranged in 2 rows. How many plants will go in each row?
Each of the rows has 386 plants.
Explanation
Divide total plants by rows.
772/2 = 386
FAQs on Factors of 772
1.What are the factors of 772?
2.Mention the prime factors of 772.
3.Is 772 a multiple of 4?
4.Mention the factor pairs of 772?
5.What is the square of 772?
Important Glossaries for Factor of 772
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 772 are 1, 2, 4, 193, 386, and 772.
- Prime factors: The factors which are prime numbers. For example, 2 and 193 are prime factors of 772.
- 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 772 are (1, 772), (2, 386), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 772 is 2² × 193.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number. For example, for 772, using the multiplication method, we identify pairs such as (1, 772) and (2, 386).
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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.
