Factors of 834

The numbers that divide 834 evenly are known as factors of 834.

A factor of 834 is a number that divides the number without a remainder.

The factors of 834 are 1, 2, 3, 6, 139, 278, 417, and 834.

Negative factors of 834: -1, -2, -3, -6, -139, -278, -417, and -834.

Prime factors of 834: 2, 3, and 139.

Prime factorization of 834: 2 × 3 × 139.

The sum of factors of 834: 1 + 2 + 3 + 6 + 139 + 278 + 417 + 834 = 1680

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 834. Identifying the numbers which are multiplied to get the number 834 is the multiplication method.

Step 1: Multiply 834 by 1, 834 × 1 = 834.

Step 2: Check for other numbers that give 834 after multiplying

2 × 417 = 834

3 × 278 = 834

6 × 139 = 834

Therefore, the positive factor pairs of 834 are: (1, 834), (2, 417), (3, 278), (6, 139).

All these factor pairs result in 834.

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 a simple division method

Step 1: Divide 834 by 1, 834 ÷ 1 = 834.

Step 2: Continue dividing 834 by the numbers until the remainder becomes 0.

834 ÷ 1 = 834

834 ÷ 2 = 417

834 ÷ 3 = 278

834 ÷ 6 = 139

Therefore, the factors of 834 are: 1, 2, 3, 6, 139, 278, 417, 834.

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 a factor tree

Using Prime Factorization: In this process, prime factors of 834 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

834 ÷ 2 = 417

417 ÷ 3 = 139

139 ÷ 139 = 1

The prime factors of 834 are 2, 3, and 139.

The prime factorization of 834 is: 2 × 3 × 139.

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

Step 1: Firstly, 834 is divided by 2 to get 417.

Step 2: Now divide 417 by 3 to get 139.

Step 3: 139 is a prime number and cannot be divided further. So, the prime factorization of 834 is: 2 × 3 × 139.

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 834: (1, 834), (2, 417), (3, 278), (6, 139).

• Negative factor pairs of 834: (-1, -834), (-2, -417), (-3, -278), (-6, -139).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 834 are 1, 2, 3, 6, 139, 278, 417, and 834.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 139 are prime factors of 834.

• 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 834 are (1, 834), (2, 417), etc.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.

• Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero.