135 LearnersLast updated on May 26th, 2025
Factors of 1770
Factors are the numbers that divide any given number evenly without a 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 1770, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1770?
The numbers that divide 1770 evenly are known as factors of 1770.
A factor of 1770 is a number that divides the number without a remainder.
The factors of 1770 are 1, 2, 3, 5, 6, 10, 15, 30, 59, 118, 177, 295, 354, 590, 885, and 1770.
Negative factors of 1770: -1, -2, -3, -5, -6, -10, -15, -30, -59, -118, -177, -295, -354, -590, -885, and -1770.
Prime factors of 1770: 2, 3, 5, and 59.
Prime factorization of 1770: 2 × 3 × 5 × 59.
The sum of factors of 1770: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 59 + 118 + 177 + 295 + 354 + 590 + 885 + 1770 = 4320
How to Find Factors of 1770?
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 1770. Identifying the numbers which are multiplied to get the number 1770 is the multiplication method.
Step 1: Multiply 1770 by 1, 1770 × 1 = 1770.
Step 2: Check for other numbers that give 1770 after multiplying
2 × 885 = 1770
3 × 590 = 1770
5 × 354 = 1770
6 × 295 = 1770
10 × 177 = 1770
15 × 118 = 1770
30 × 59 = 1770
Therefore, the positive factor pairs of 1770 are: (1, 1770), (2, 885), (3, 590), (5, 354), (6, 295), (10, 177), (15, 118), and (30, 59).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers 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 the simple division method
Step 1: Divide 1770 by 1, 1770 ÷ 1 = 1770.
Step 2: Continue dividing 1770 by the numbers until the remainder becomes 0.
1770 ÷ 1 = 1770
1770 ÷ 2 = 885
1770 ÷ 3 = 590
1770 ÷ 5 = 354
1770 ÷ 6 = 295
1770 ÷ 10 = 177
1770 ÷ 15 = 118
1770 ÷ 30 = 59
Therefore, the factors of 1770 are: 1, 2, 3, 5, 6, 10, 15, 30, 59, 118, 177, 295, 354, 590, 885, and 1770.
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 1770 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1770 ÷ 2 = 885
885 ÷ 3 = 295
295 ÷ 5 = 59
59 ÷ 59 = 1
The prime factors of 1770 are 2, 3, 5, and 59.
The prime factorization of 1770 is: 2 × 3 × 5 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1770 is divided by 2 to get 885.
Step 2: Now divide 885 by 3 to get 295.
Step 3: Then divide 295 by 5 to get 59. Here, 59 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1770 is: 2 × 3 × 5 × 59.
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 1770: (1, 1770), (2, 885), (3, 590), (5, 354), (6, 295), (10, 177), (15, 118), and (30, 59).
Negative factor pairs of 1770: (-1, -1770), (-2, -885), (-3, -590), (-5, -354), (-6, -295), (-10, -177), (-15, -118), and (-30, -59).
Common Mistakes and How to Avoid Them in Factors of 1770
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 1770, 1 and 1770 are also factors.
Mistake 2
Missing Negative Factors
We have used only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1770 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1770/1.5 = 1180, 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 1770 are prime numbers.
For example, 2, 3, 5, and 59 are the prime factors of 1770, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1770 as 2 × 3 × 5 × 59 and missing all the key factors.
Factors of 1770 Examples
Problem 1
There are 30 students, and each has 59 candies. How many candies are there in total?
There are 1770 candies in total.
Explanation
To find the total candies, we multiply the number of students by the number of candies each student has.
30 × 59 = 1770
Problem 2
A garden is rectangular, the width of the garden is 10 meters and the total area is 1770 square meters. Find the length?
177 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1770 = length × 10
To find the value of the length, we need to divide 1770 by 10.
1770/10 = length
Length = 177.
Problem 3
There are 1770 toys and 59 boxes. How many toys will be in each box?
Each box will have 30 toys.
Explanation
To find the toys in each box, divide the total toys by the number of boxes.
1770/59 = 30
Problem 4
In a company, there are 1770 employees, and 6 departments. How many employees are there in each department?
There are 295 employees in each department.
Explanation
Dividing the employees by the total departments, we will get the number of employees in each department.
1770/6 = 295
Problem 5
1770 chairs need to be arranged in 15 sections. How many chairs will go in each section?
Each of the sections has 118 chairs.
Explanation
Divide total chairs by sections.
1770/15 = 118
FAQs on Factors of 1770
1.What are the factors of 1770?
2.Mention the prime factors of 1770.
3.Is 1770 a multiple of 10?
4.Mention the factor pairs of 1770?
5.What is the square of 1770?
6.How can children in United States use numbers in everyday life to understand Factors of 1770?
7.What are some fun ways kids in United States can practice Factors of 1770 with numbers?
8.What role do numbers and Factors of 1770 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1770 skills?
Important Glossaries for Factors of 1770
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1770 are 1, 2, 3, 5, 6, 10, 15, 30, 59, 118, 177, 295, 354, 590, 885, and 1770.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 59 are prime factors of 1770.
- 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 1770 are (1, 1770), (2, 885), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1770 is 2 × 3 × 5 × 59.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to give the original number. For example, using this method to find factors of 1770.
Explore More numbers
About BrightChamps in United States
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.
