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

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

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
• 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.

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).

• 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.