Factors of 846

The numbers that divide 846 evenly are known as factors of 846.

A factor of 846 is a number that divides the number without remainder.

The factors of 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, and 846.

Negative factors of 846: -1, -2, -3, -6, -9, -18, -47, -94, -141, -282, -423, and -846.

Prime factors of 846: 2, 3, and 47.

Prime factorization of 846: 2 × 3^2 × 47.

The sum of factors of 846: 1 + 2 + 3 + 6 + 9 + 18 + 47 + 94 + 141 + 282 + 423 + 846 = 1872

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 846. Identifying the numbers which are multiplied to get the number 846 is the multiplication method.

Step 1: Multiply 846 by 1, 846 × 1 = 846.

Step 2: Check for other numbers that give 846 after multiplying

2 × 423 = 846

3 × 282 = 846

6 × 141 = 846

9 × 94 = 846

18 × 47 = 846

Therefore, the positive factor pairs of 846 are: (1, 846), (2, 423), (3, 282), (6, 141), (9, 94), (18, 47). All these factor pairs result in 846. 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 that result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 846 by 1, 846 ÷ 1 = 846.

Step 2: Continue dividing 846 by the numbers until the remainder becomes 0.

846 ÷ 1 = 846

846 ÷ 2 = 423

846 ÷ 3 = 282

846 ÷ 6 = 141

846 ÷ 9 = 94

846 ÷ 18 = 47

Therefore, the factors of 846 are: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846.

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

846 ÷ 2 = 423

423 ÷ 3 = 141

141 ÷ 3 = 47

47 ÷ 47 = 1

The prime factors of 846 are 2, 3, and 47.

The prime factorization of 846 is: 2 × 3² × 47.

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

Step 1: Firstly, 846 is divided by 2 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 the smallest prime number, that cannot be divided anymore. So, the prime factorization of 846 is: 2 × 3^2 × 47.

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 846: (1, 846), (2, 423), (3, 282), (6, 141), (9, 94), (18, 47).

• Negative factor pairs of 846: (-1, -846), (-2, -423), (-3, -282), (-6, -141), (-9, -94), (-18, -47).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, and 846.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 47 are prime factors of 846.

• 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 846 are (1, 846), (2, 423), etc.

• Multiplication method: A method of finding factors by identifying pairs of numbers that can be multiplied to get the original number.

• Division method: A method of finding factors by dividing the number by integers and checking for a zero remainder.