Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find the number of participants in each row, divide the total participants by the number of rows.
1230/30 = 41
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.
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.
A factory produces 2460 widgets in 2 days. How many widgets are produced each day?
1230 widgets each day.
To find the widgets produced each day, divide the total widgets by the number of days.
2460/2 = 1230
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.
Dividing the total points by the number of teams gives the average points scored by each team.
1230/5 = 246
A shipment contains 615 boxes, and each box holds 2 items. How many items are there in total?
1230 items.
Multiply the number of boxes by the number of items per box to find the total items.
615 × 2 = 1230
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.
: She loves to read number jokes and games.