115 LearnersLast updated on May 26th, 2025
Factors of 1710
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 1710, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1710?
The numbers that divide 1710 evenly are known as factors of 1710.
A factor of 1710 is a number that divides the number without remainder.
The factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 51, 85, 90, 102, 153, 170, 255, 285, 342, 510, 855, and 1710.
Negative factors of 1710: -1, -2, -3, -5, -6, -9, -10, -15, -17, -18, -30, -34, -51, -85, -90, -102, -153, -170, -255, -285, -342, -510, -855, and -1710.
Prime factors of 1710: 2, 3, 5, and 19.
Prime factorization of 1710: 2 × 3 × 5 × 19.
The sum of factors of 1710: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 17 + 18 + 30 + 34 + 51 + 85 + 90 + 102 + 153 + 170 + 255 + 285 + 342 + 510 + 855 + 1710 = 4965
How to Find Factors of 1710?
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 1710. Identifying the numbers which are multiplied to get the number 1710 is the multiplication method.
Step 1: Multiply 1710 by 1, 1710 × 1 = 1710.
Step 2: Check for other numbers that give 1710 after multiplying
2 × 855 = 1710
3 × 570 = 1710
5 × 342 = 1710
6 × 285 = 1710
9 × 190 = 1710
10 × 171 = 1710
15 × 114 = 1710
17 × 100 = 1710
18 × 95 = 1710
30 × 57 = 1710
34 × 50 = 1710
51 × 35 = 1710
Therefore, the positive factor pairs of 1710 are: (1, 1710), (2, 855), (3, 570), (5, 342), (6, 285), (9, 190), (10, 171), (15, 114), (17, 100), (18, 95), (30, 57), (34, 50), (51, 35).
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 a simple division method
Step 1: Divide 1710 by 1, 1710 ÷ 1 = 1710.
Step 2: Continue dividing 1710 by the numbers until the remainder becomes 0.
1710 ÷ 1 = 1710
1710 ÷ 2 = 855
1710 ÷ 3 = 570
1710 ÷ 5 = 342
1710 ÷ 6 = 285
1710 ÷ 9 = 190
1710 ÷ 10 = 171
1710 ÷ 15 = 114
1710 ÷ 17 = 100
1710 ÷ 18 = 95
1710 ÷ 30 = 57
1710 ÷ 34 = 50
1710 ÷ 51 = 35
Therefore, the factors of 1710 are: 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 51, 85, 90, 102, 153, 170, 255, 285, 342, 510, 855, 1710.
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 1710 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1710 ÷ 2 = 855
855 ÷ 3 = 285
285 ÷ 3 = 95
95 ÷ 5 = 19
19 ÷ 19 = 1
The prime factors of 1710 are 2, 3, 5, and 19.
The prime factorization of 1710 is: 2 × 3 × 5 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1710 is divided by 2 to get 855.
Step 2: Now divide 855 by 3 to get 285.
Step 3: Then divide 285 by 3 to get 95.
Step 4: Divide 95 by 5 to get 19. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1710 is: 2 × 3 × 5 × 19.
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 1710: (1, 1710), (2, 855), (3, 570), (5, 342), (6, 285), (9, 190), (10, 171), (15, 114), (17, 100), (18, 95), (30, 57), (34, 50), (51, 35).
Negative factor pairs of 1710: (-1, -1710), (-2, -855), (-3, -570), (-5, -342), (-6, -285), (-9, -190), (-10, -171), (-15, -114), (-17, -100), (-18, -95), (-30, -57), (-34, -50), (-51, -35).
Common Mistakes and How to Avoid Them in Factors of 1710
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
People 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 1710, 1 and 1710 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 1710 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1710/1.5 = 1140, 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 1710 are prime numbers.
For example, 2, 3, 5, and 19 are the prime factors of 1710, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
People might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1710 as 2 × 3 × 5 × 19 and missing all the key factors.
Factors of 1710 Examples
Problem 1
There are 9 friends and 1710 candies. How will they divide it equally?
They will get 190 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1710/9 = 190
Problem 2
A field is rectangular, the length of the field is 30 meters and the total area is 1710 square meters. Find the width?
57 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1710 = 30 × width
To find the value of width, we need to shift 30 to the left side.
1710/30 = width
Width = 57.
Problem 3
There are 51 bags and 1710 marbles. How many marbles will be in each bag?
Each bag will have 35 marbles.
Explanation
To find the marbles in each bag, divide the total marbles with the bags.
1710/51 = 35
Problem 4
In a class, there are 1710 students, and 10 groups. How many students are there in each group?
There are 171 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1710/10 = 171
Problem 5
1710 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has 114 books.
Explanation
Divide total books with shelves.
1710/15 = 114
FAQs on Factors of 1710
1.What are the factors of 1710?
2.Mention the prime factors of 1710.
3.Is 1710 a multiple of 3?
4.Mention the factor pairs of 1710?
5.What is the square of 1710?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1710?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1710 with numbers?
8.What role do numbers and Factors of 1710 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 1710 skills?
Important Glossaries for Factor of 1710
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1710 are 1, 2, 3, 5, 6, ..., 1710.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 19 are prime factors of 1710.
- 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 1710 are (1, 1710), (2, 855), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1710 is 2 × 3 × 5 × 19.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1710 is a multiple of 3.
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About BrightChamps in United Arab Emirates
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.
