136 LearnersLast updated on May 30th, 2025
Factors of 1210
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 1210, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1210?
The numbers that divide 1210 evenly are known as factors of 1210.
A factor of 1210 is a number that divides the number without remainder.
The factors of 1210 are 1, 2, 5, 11, 22, 55, 110, 121, 242, 605, and 1210.
Negative factors of 1210: -1, -2, -5, -11, -22, -55, -110, -121, -242, -605, and -1210.
Prime factors of 1210: 2, 5, and 11. Prime factorization of 1210: 2 × 5 × 112.
The sum of factors of 1210: 1 + 2 + 5 + 11 + 22 + 55 + 110 + 121 + 242 + 605 + 1210 = 2384
How to Find Factors of 1210?
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 1210. Identifying the numbers which are multiplied to get the number 1210 is the multiplication method.
Step 1: Multiply 1210 by 1, 1210 × 1 = 1210.
Step 2: Check for other numbers that give 1210 after multiplying
2 × 605 = 1210
5 × 242 = 1210
10 × 121 = 1210
11 × 110 = 1210
22 × 55 = 1210
Therefore, the positive factor pairs of 1210 are: (1, 1210), (2, 605), (5, 242), (10, 121), (11, 110), (22, 55). 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 1210 by 1, 1210 ÷ 1 = 1210.
Step 2: Continue dividing 1210 by the numbers until the remainder becomes 0.
1210 ÷ 1 = 1210
1210 ÷ 2 = 605
1210 ÷ 5 = 242
1210 ÷ 10 = 121
1210 ÷ 11 = 110
1210 ÷ 22 = 55
Therefore, the factors of 1210 are: 1, 2, 5, 11, 22, 55, 110, 121, 242, 605, 1210.
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 1210 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1210 ÷ 2 = 605
605 ÷ 5 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factors of 1210 are 2, 5, and 11.
The prime factorization of 1210 is: 2 × 5 × 112.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1210 is divided by 2 to get 605.
Step 2: Now divide 605 by 5 to get 121.
Step 3: Then divide 121 by 11 to get 11.
Step 4: Divide 11 by 11 to get 1. So, the prime factorization of 1210 is: 2 × 5 × 112.
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 1210: (1, 1210), (2, 605), (5, 242), (10, 121), (11, 110), (22, 55).
Negative factor pairs of 1210: (-1, -1210), (-2, -605), (-5, -242), (-10, -121), (-11, -110), (-22, -55).
Common Mistakes and How to Avoid Them in Factors of 1210
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 1210, 1 and 1210 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 1210 include -1, -2, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1210/1.5 = 806.666, 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 1210 are prime numbers. For example, 2, 5, and 11 are the prime factors of 1210, but it has other factors like 22, 110.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1210 as 2 × 5 × 11^2 and missing all the key factors.
Factors of 1210 Examples
Problem 1
There are 110 chairs and 1210 balloons. How will they distribute them equally?
They will put 11 balloons on each chair.
Explanation
To distribute the balloons equally, we need to divide the total balloons with the number of chairs.
1210/110 = 11
Problem 2
A garden is rectangular, the length of the garden is 22 meters and the total area is 1210 square meters. Find the width?
55 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1210 = 22 × width
To find the value of width, we need to shift 22 to the left side.
1210/22 = width
Width = 55.
Problem 3
There are 11 baskets and 1210 apples. How many apples will be in each basket?
Each basket will have 110 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1210/11 = 110
Problem 4
In a conference, there are 1210 attendees, and 11 groups. How many attendees are there in each group?
There are 110 attendees in each group.
Explanation
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1210/11 = 110
Problem 5
1210 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 242 books.
Explanation
Divide total books by shelves.
1210/5 = 242
FAQs on Factors of 1210
1.What are the factors of 1210?
2.Mention the prime factors of 1210.
3.Is 1210 a multiple of 11?
4.Mention the factor pairs of 1210?
5.What is the square of 1210?
6.How can children in United States use numbers in everyday life to understand Factors of 1210?
7.What are some fun ways kids in United States can practice Factors of 1210 with numbers?
8.What role do numbers and Factors of 1210 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 1210 skills?
Important Glossaries for Factors of 1210
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1210 are 1, 2, 5, 11, 22, 55, 110, 121, 242, 605, and 1210.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 11 are prime factors of 1210.
- 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 1210 are (1, 1210), (2, 605), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1210 is 2 × 5 × 112.
- Negative factors: These are the negative counterparts of the positive factors of a number. For example, the negative factors of 1210 are -1, -2, -5, -11, -22, -55, -110, -121, -242, -605, and -1210.
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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
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