Factors of 1236

The numbers that divide 1236 evenly are known as factors of 1236. A factor of 1236 is a number that divides the number without remainder. The factors of 1236 are 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, and 1236.

Negative factors of 1236: -1, -2, -3, -4, -6, -12, -103, -206, -309, -412, -618, and -1236.

Prime factors of 1236: 2 and 3.

Prime factorization of 1236: 2² × 3¹ × 103¹.

The sum of factors of 1236: 1 + 2 + 3 + 4 + 6 + 12 + 103 + 206 + 309 + 412 + 618 + 1236 = 2912

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1236. Identifying the numbers which are multiplied to get the number 1236 is the multiplication method.

Step 1: Multiply 1236 by 1, 1236 × 1 = 1236.

Step 2: Check for other numbers that give 1236 after multiplying

2 × 618 = 1236

3 × 412 = 1236

4 × 309 = 1236

6 × 206 = 1236

12 × 103 = 1236

Therefore, the positive factor pairs of 1236 are: (1, 1236), (2, 618), (3, 412), (4, 309), (6, 206), and (12, 103). For every positive factor, there is a negative factor.

Dividing the given numbers with 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 1236 by 1, 1236 ÷ 1 = 1236.

Step 2: Continue dividing 1236 by the numbers until the remainder becomes 0.

1236 ÷ 1 = 1236

1236 ÷ 2 = 618

1236 ÷ 3 = 412

1236 ÷ 4 = 309

1236 ÷ 6 = 206

1236 ÷ 12 = 103

Therefore, the factors of 1236 are: 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, and 1236.

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 1236 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1236 ÷ 2 = 618

618 ÷ 2 = 309

309 ÷ 3 = 103

103 ÷ 103 = 1

The prime factors of 1236 are 2, 3, and 103. The prime factorization of 1236 is: 2² × 3¹ × 103¹.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 1236 is divided by 2 to get 618.

Step 2: Now divide 618 by 2 to get 309.

Step 3: Then divide 309 by 3 to get 103. Here, 103 is a prime number that cannot be divided anymore. So, the prime factorization of 1236 is: 2² × 3¹ × 103¹.

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 1236: (1, 1236), (2, 618), (3, 412), (4, 309), (6, 206), and (12, 103).

• Negative factor pairs of 1236: (-1, -1236), (-2, -618), (-3, -412), (-4, -309), (-6, -206), and (-12, -103).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1236 are 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, and 1236.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 103 are prime factors of 1236.

• 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 1236 are (1, 1236), (2, 618), etc.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1236 is 2² × 3¹ × 103¹.

• Multiplication Method: A method to determine factors by identifying pairs of numbers that multiply to form the original number. For example, using multiplication to find factors of 1236.