Factors of 1146

The numbers that divide 1146 evenly are known as factors of 1146. A factor of 1146 is a number that divides the number without remainder. The factors of 1146 are 1, 2, 3, 6, 9, 18, 31, 62, 57, 93, 186, 381, 573, and 1146.

Negative factors of 1146: -1, -2, -3, -6, -9, -18, -31, -62, -57, -93, -186, -381, -573, and -1146.

Prime factors of 1146: 2, 3, and 191.

Prime factorization of 1146: 2 × 3 × 191.

The sum of factors of 1146: 1 + 2 + 3 + 6 + 9 + 18 + 31 + 62 + 57 + 93 + 186 + 381 + 573 + 1146 = 2568.

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 1146. Identifying the numbers which are multiplied to get the number 1146 is the multiplication method.

Step 1: Multiply 1146 by 1, 1146 × 1 = 1146.

Step 2: Check for other numbers that give 1146 after multiplying

2 × 573 = 1146

3 × 382 = 1146

6 × 191 = 1146

9 × 127 = 1146

18 × 63.67 = 1146 (but 63.67 is not a whole number, so it's not a factor pair)

31 × 37 = 1146

Therefore, the positive factor pairs of 1146 are: (1, 1146), (2, 573), (3, 382), (6, 191), (9, 127), (31, 37). All these factor pairs result in 1146. 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 1146 by 1, 1146 ÷ 1 = 1146.

Step 2: Continue dividing 1146 by the numbers until the remainder becomes 0.

1146 ÷ 1 = 1146

1146 ÷ 2 = 573

1146 ÷ 3 = 382

1146 ÷ 6 = 191

1146 ÷ 9 = 127

1146 ÷ 31 = 37

Therefore, the factors of 1146 are: 1, 2, 3, 6, 9, 31, 37, 62, 114, 186, 381, 573, and 1146.

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 1146 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

1146 ÷ 2 = 573

573 ÷ 3 = 191

191 is a prime number.

The prime factors of 1146 are 2, 3, and 191. The prime factorization of 1146 is: 2 × 3 × 191.

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

Step 1: Firstly, 1146 is divided by 2 to get 573.

Step 2: Now divide 573 by 3 to get 191.

Step 3: 191 is a prime number and cannot be divided further by any number other than 1 and itself. So, the prime factorization of 1146 is: 2 × 3 × 191.

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 1146: (1, 1146), (2, 573), (3, 382), (6, 191), (9, 127), and (31, 37).
• Negative factor pairs of 1146: (-1, -1146), (-2, -573), (-3, -382), (-6, -191), (-9, -127), and (-31, -37).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1146 are 1, 2, 3, 6, 9, 31, 37, and 1146.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 191 are prime factors of 1146.

• 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 1146 are (1, 1146), (2, 573), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For 1146, it is 2 × 3 × 191.

• Multiple: A number that can be divided by another number without a remainder. For example, 1146 is a multiple of 9.