121 LearnersLast updated on May 26th, 2025
Factors of 770
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 770, how they are used in real life, and tips to learn them quickly.
What are the Factors of 770?
The numbers that divide 770 evenly are known as factors of 770.
A factor of 770 is a number that divides the number without remainder.
The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, and 770.
Negative factors of 770: -1, -2, -5, -7, -10, -11, -14, -22, -35, -55, -70, -77, -110, -154, -385, and -770.
Prime factors of 770: 2, 5, 7, and 11.
Prime factorization of 770: 2 × 5 × 7 × 11.
The sum of factors of 770: 1 + 2 + 5 + 7 + 10 + 11 + 14 + 22 + 35 + 55 + 70 + 77 + 110 + 154 + 385 + 770 = 1728.
How to Find Factors of 770?
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 770. Identifying the numbers which are multiplied to get the number 770 is the multiplication method.
Step 1: Multiply 770 by 1, 770 × 1 = 770.
Step 2: Check for other numbers that give 770 after multiplying
2 × 385 = 770
5 × 154 = 770
7 × 110 = 770
10 × 77 = 770
11 × 70 = 770
14 × 55 = 770
22 × 35 = 770
Therefore, the positive factor pairs of 770 are: (1, 770), (2, 385), (5, 154), (7, 110), (10, 77), (11, 70), (14, 55), (22, 35). All these factor pairs result in 770.
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 770 by 1, 770 ÷ 1 = 770.
Step 2: Continue dividing 770 by the numbers until the remainder becomes 0.
770 ÷ 1 = 770
770 ÷ 2 = 385
770 ÷ 5 = 154
770 ÷ 7 = 110
770 ÷ 10 = 77
770 ÷ 11 = 70
770 ÷ 14 = 55
770 ÷ 22 = 35
Therefore, the factors of 770 are: 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770.
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 770 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
770 ÷ 2 = 385
385 ÷ 5 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 770 are 2, 5, 7, and 11.
The prime factorization of 770 is: 2 × 5 × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 770 is divided by 2 to get 385.
Step 2: Now divide 385 by 5 to get 77.
Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 770 is: 2 × 5 × 7 × 11.
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 770: (1, 770), (2, 385), (5, 154), (7, 110), (10, 77), (11, 70), (14, 55), and (22, 35).
Negative factor pairs of 770: (-1, -770), (-2, -385), (-5, -154), (-7, -110), (-10, -77), (-11, -70), (-14, -55), and (-22, -35).
Common Mistakes and How to Avoid Them in Factors of 770
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 770, 1 and 770 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 770 consist of -1, -2, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 770/1.5 = 513.333, 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 770 are prime numbers.
For example, 2, 5, 7, and 11 are the prime factors of 770, but it has other factors like 10, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 770 as 2 × 5 × 7 × 11 and missing all the key factors.
Factors of 770 Examples
Problem 1
There are 11 teams and 770 participants. How will they be divided equally among the teams?
They will have 70 participants each.
Explanation
To divide the participants equally, we need to divide the total participants with the number of teams.
770/11 = 70
Problem 2
A rectangular plot has a width of 14 meters and a total area of 770 square meters. Find the length.
55 meters.
Explanation
To find the length of the plot, we use the formula,
Area = length × width
770 = length × 14
To find the value of length, we need to shift 14 to the left side.
770/14 = length
Length = 55.
Problem 3
There are 35 boxes and 770 apples. How many apples will be in each box?
Each box will have 22 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
770/35 = 22
Problem 4
In a class, there are 770 students, and 10 groups. How many students are there in each group?
There are 77 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
770/10 = 77
Problem 5
770 books need to be arranged in 14 shelves. How many books will go on each shelf?
Each of the shelves has 55 books.
Explanation
Divide total books with shelves.
770/14 = 55
FAQs on Factors of 770
1.What are the factors of 770?
2.Mention the prime factors of 770.
3.Is 770 a multiple of 11?
4.Mention the factor pairs of 770?
5.What is the square of 770?
Important Glossaries for Factors of 770
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, and 770.
- Prime factors: The factors which are prime numbers. For example, 2, 5, 7, and 11 are prime factors of 770.
- 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 770 are (1, 770), (2, 385), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 770 is 2 × 5 × 7 × 11.
- Negative factors: The negative counterparts of positive factors. For example, -1, -2, -5, -7, -10, -11, -14, -22, -35, -55, -70, -77, -110, -154, -385, and -770 are the negative factors of 770.
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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.
