Factors of 837

The numbers that divide 837 evenly are known as factors of 837.

A factor of 837 is a number that divides the number without a remainder.

The factors of 837 are 1, 3, 9, 27, 31, 93, 279, and 837.

Negative factors of 837: -1, -3, -9, -27, -31, -93, -279, and -837.

Prime factors of 837: 3 and 31.

Prime factorization of 837: 3³ × 31.

The sum of factors of 837: 1 + 3 + 9 + 27 + 31 + 93 + 279 + 837 = 1240

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

• Finding factors using multiplication
   
• Finding factors using division method
   
• Prime factors and prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 837. Identifying the numbers which are multiplied to get the number 837 is the multiplication method.

Step 1: Multiply 837 by 1, 837 × 1 = 837.

Step 2: Check for other numbers that give 837 after multiplying

3 × 279 = 837

9 × 93 = 837

27 × 31 = 837

Therefore, the positive factor pairs of 837 are: (1, 837), (3, 279), (9, 93), and (27, 31).

All these factor pairs result in 837.

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 837 by 1, 837 ÷ 1 = 837.

Step 2: Continue dividing 837 by the numbers until the remainder becomes 0.

837 ÷ 1 = 837

837 ÷ 3 = 279

837 ÷ 9 = 93

837 ÷ 27 = 31

Therefore, the factors of 837 are: 1, 3, 9, 27, 31, 93, 279, 837.

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

837 ÷ 3 = 279

279 ÷ 3 = 93

93 ÷ 3 = 31

31 ÷ 31 = 1

The prime factors of 837 are 3 and 31.

The prime factorization of 837 is: 3³ × 31.

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

Step 1: Firstly, 837 is divided by 3 to get 279.

Step 2: Now divide 279 by 3 to get 93.

Step 3: Then divide 93 by 3 to get 31. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 837 is: 3³ × 31.

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 837: (1, 837), (3, 279), (9, 93), and (27, 31).

• Negative factor pairs of 837: (-1, -837), (-3, -279), (-9, -93), and (-27, -31).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 837 are 1, 3, 9, 27, 31, 93, 279, and 837.

• Prime factors: The factors which are prime numbers. For example, 3 and 31 are prime factors of 837.

• 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 837 are (1, 837), (3, 279), etc.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 837 is 3³ × 31.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, 9 × 93 = 837 is a factor pair.