Factors of 1272

The numbers that divide 1272 evenly are known as factors of 1272. A factor of 1272 is a number that divides the number without a remainder. The factors of 1272 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.

Negative factors of 1272: -1, -2, -3, -4, -6, -12, -53, -106, -159, -212, -318, -636, and -1272.

Prime factors of 1272: 2, 3, and 53.

Prime factorization of 1272: 2² × 3 × 53.

The sum of factors of 1272: 1 + 2 + 3 + 4 + 6 + 12 + 53 + 106 + 159 + 212 + 318 + 636 + 1272 = 2784

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

1. Finding factors using multiplication
2. Finding factors using the 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 1272. Identifying the numbers which are multiplied to get the number 1272 is the multiplication method.

Step 1: Multiply 1272 by 1, 1272 × 1 = 1272.

Step 2: Check for other numbers that give 1272 after multiplying

2 × 636 = 1272

3 × 424 = 1272

4 × 318 = 1272

6 × 212 = 1272

12 × 106 = 1272

53 × 24 = 1272

Therefore, the positive factor pairs of 1272 are: (1, 1272), (2, 636), (3, 424), (4, 318), (6, 212), (12, 106), and (53, 24). For each 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 a simple division method -

Step 1: Divide 1272 by 1, 1272 ÷ 1 = 1272.

Step 2: Continue dividing 1272 by the numbers until the remainder becomes 0.

1272 ÷ 1 = 1272

1272 ÷ 2 = 636

1272 ÷ 3 = 424

1272 ÷ 4 = 318

1272 ÷ 6 = 212

1272 ÷ 12 = 106

1272 ÷ 53 = 24

Therefore, the factors of 1272 are: 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.

The factors can be found by dividing them 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 1272 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1272 ÷ 2 = 636

636 ÷ 2 = 318

318 ÷ 3 = 106

106 ÷ 53 = 2

2 ÷ 1 = 0

The prime factors of 1272 are 2, 3, and 53. The prime factorization of 1272 is: 2² × 3 × 53.

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

Step 1: Firstly, 1272 is divided by 2 to get 636.

Step 2: Now divide 636 by 2 to get 318.

Step 3: Then divide 318 by 3 to get 106.

Step 4: Divide 106 by 53 to get 2. Here, 53 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1272 is: 2² × 3 × 53.

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 1272: (1, 1272), (2, 636), (3, 424), (4, 318), (6, 212), (12, 106), and (53, 24).

• Negative factor pairs of 1272: (-1, -1272), (-2, -636), (-3, -424), (-4, -318), (-6, -212), (-12, -106), and (-53, -24).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1272 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 53 are prime factors of 1272.

• 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 1272 are (1, 1272), (2, 636), etc.

• Prime factorization: The process of expressing a number as a product of its prime factors. For 1272, it is 2² × 3 × 53.

• Multiple: A number that can be divided by another number without leaving a remainder. For example, 1272 is a multiple of 4.