Factors of 1269

The numbers that divide 1269 evenly are known as factors of 1269. A factor of 1269 is a number that divides the number without a remainder. The factors of 1269 are 1, 3, 13, 39, 423, and 1269.

Negative factors of 1269: -1, -3, -13, -39, -423, and -1269.

Prime factors of 1269: 3 and 13.

Prime factorization of 1269: 3 × 13 × 3 × 13.

The sum of factors of 1269: 1 + 3 + 13 + 39 + 423 + 1269 = 1748

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 1269. Identifying the numbers which are multiplied to get the number 1269 is the multiplication method.

Step 1: Multiply 1269 by 1, 1269 × 1 = 1269.

Step 2: Check for other numbers that give 1269 after multiplying

3 × 423 = 1269

13 × 39 = 1269

Therefore, the positive factor pairs of 1269 are: (1, 1269), (3, 423), (13, 39). All these factor pairs result in 1269. 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 a simple division method -

Step 1: Divide 1269 by 1, 1269 ÷ 1 = 1269.

Step 2: Continue dividing 1269 by the numbers until the remainder becomes 0.

1269 ÷ 1 = 1269

1269 ÷ 3 = 423

1269 ÷ 13 = 39

Therefore, the factors of 1269 are: 1, 3, 13, 39, 423, 1269.

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 1269 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

1269 ÷ 3 = 423

423 ÷ 3 = 141

141 ÷ 3 = 47

47 ÷ 47 = 1

The prime factors of 1269 are 3 and 13. The prime factorization of 1269 is: 3 × 13 × 3 × 13.

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

Step 1: Firstly, 1269 is divided by 3 to get 423.

Step 2: Now divide 423 by 3 to get 141.

Step 3: Then divide 141 by 3 to get 47. Here, 47 is a prime number, which cannot be divided anymore. So, the prime factorization of 1269 is: 3 × 13 × 3 × 13.

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 1269: (1, 1269), (3, 423), (13, 39).

• Negative factor pairs of 1269: (-1, -1269), (-3, -423), (-13, -39).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1269 are 1, 3, 13, 39, 423, and 1269.

• Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 1269.

• 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 1269 are (1, 1269), (3, 423), etc.

• Prime factorization: Breaking down a number into its prime factors, for example, the prime factorization of 1269 is 3 × 13 × 3 × 13.

• Multiple: A number that can be divided by another number without a remainder, for example, 1269 is a multiple of 3.