143 LearnersLast updated on May 26th, 2025
Factors of 1230
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 1230, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1230?
The numbers that divide 1230 evenly are known as factors of 1230. A factor of 1230 is a number that divides the number without remainder. The factors of 1230 are 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, and 1230.
Negative factors of 1230: -1, -2, -3, -5, -6, -10, -15, -30, -41, -82, -123, -205, -246, -410, -615, and -1230.
Prime factors of 1230: 2, 3, 5, and 41.
Prime factorization of 1230: 2 × 3 × 5 × 41.
The sum of factors of 1230: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 41 + 82 + 123 + 205 + 246 + 410 + 615 + 1230 = 3024
How to Find Factors of 1230?
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 1230. Identifying the numbers which are multiplied to get the number 1230 is the multiplication method.
Step 1: Multiply 1230 by 1, 1230 × 1 = 1230.
Step 2: Check for other numbers that give 1230 after multiplying
2 × 615 = 1230
3 × 410 = 1230
5 × 246 = 1230
6 × 205 = 1230
10 × 123 = 1230
15 × 82 = 1230
30 × 41 = 1230
Therefore, the positive factor pairs of 1230 are: (1, 1230), (2, 615), (3, 410), (5, 246), (6, 205), (10, 123), (15, 82), (30, 41). 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 1230 by 1, 1230 ÷ 1 = 1230.
Step 2: Continue dividing 1230 by the numbers until the remainder becomes 0.
1230 ÷ 1 = 1230
1230 ÷ 2 = 615
1230 ÷ 3 = 410
1230 ÷ 5 = 246
1230 ÷ 6 = 205
1230 ÷ 10 = 123
1230 ÷ 15 = 82
1230 ÷ 30 = 41
Therefore, the factors of 1230 are: 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, 1230.
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 1230 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1230 ÷ 2 = 615
615 ÷ 3 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1
The prime factors of 1230 are 2, 3, 5, and 41. The prime factorization of 1230 is: 2 × 3 × 5 × 41.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1230 is divided by 2 to get 615.
Step 2: Now divide 615 by 3 to get 205.
Step 3: Then divide 205 by 5 to get 41. Here, 41 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1230 is: 2 × 3 × 5 × 41.
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 1230: (1, 1230), (2, 615), (3, 410), (5, 246), (6, 205), (10, 123), (15, 82), (30, 41).
- Negative factor pairs of 1230: (-1, -1230), (-2, -615), (-3, -410), (-5, -246), (-6, -205), (-10, -123), (-15, -82), (-30, -41).
Common Mistakes and How to Avoid Them in Factors of 1230
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 1230, 1 and 1230 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 1230 consist of -1, -2, -3, 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 1230/1.5 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 1230 are prime numbers. For example, 2, 3, 5, and 41 are the prime factors of 1230, 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 1230 as 2 × 3 × 5 × 41 and missing all the key factors.
Factors of 1230 Examples
Problem 1
A group of 1230 participants needs to be seated in a hall with 30 rows. How many participants will be seated in each row?
41 participants in each row.
Explanation
To find the number of participants in each row, divide the total participants by the number of rows.
1230/30 = 41
Problem 2
A rectangular plot has a length of 82 meters and a total area of 1230 square meters. What is the width of the plot?
15 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1230 = 82 × width
To find the value of width, we need to shift 82 to the left side.
1230/82 = width
Width = 15.
Problem 3
A factory produces 2460 widgets in 2 days. How many widgets are produced each day?
1230 widgets each day.
Explanation
To find the widgets produced each day, divide the total widgets by the number of days.
2460/2 = 1230
Problem 4
There are 5 teams in a tournament, and a total of 1230 points are scored. How many points did each team score on average?
246 points per team.
Explanation
Dividing the total points by the number of teams gives the average points scored by each team.
1230/5 = 246
Problem 5
A shipment contains 615 boxes, and each box holds 2 items. How many items are there in total?
1230 items.
Explanation
Multiply the number of boxes by the number of items per box to find the total items.
615 × 2 = 1230
FAQs on Factors of 1230
1.What are the factors of 1230?
2.Mention the prime factors of 1230.
3.Is 1230 a multiple of 10?
4.Mention the factor pairs of 1230?
5.What is the square of 1230?
Important Glossaries for Factors of 1230
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1230 are 1, 2, 3, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 41 are prime factors of 1230.
- 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 1230 are (1, 1230), (2, 615), etc.
- Prime factorization: Breaking down a number into its prime components. For 1230, it is 2 × 3 × 5 × 41.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number, such as 1230.
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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.
