Factors of 841

The numbers that divide 841 evenly are known as factors of 841.

A factor of 841 is a number that divides the number without remainder.

The factors of 841 are 1, 29, and 841.

Negative factors of 841: -1, -29, and -841.

Prime factors of 841: 29.

Prime factorization of 841: 29 × 29 or 29².

The sum of factors of 841: 1 + 29 + 841 = 871

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 841. Identifying the numbers which are multiplied to get the number 841 is the multiplication method.

Step 1: Multiply 841 by 1, 841 × 1 = 841.

Step 2: Check for other numbers that give 841 after multiplying 29 × 29 = 841

Therefore, the positive factor pairs of 841 are: (1, 841) and (29, 29).

For every positive factor, there is a negative factor.

Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method

Step 1: Divide 841 by 1, 841 ÷ 1 = 841.

Step 2: Continue dividing 841 by the numbers until the remainder becomes 0.

841 ÷ 1 = 841

841 ÷ 29 = 29

Therefore, the factors of 841 are: 1, 29, and 841.

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

841 ÷ 29 = 29

29 ÷ 29 = 1

The prime factor of 841 is 29.

The prime factorization of 841 is: 29 × 29 or 29².

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

Step 1: Firstly, 841 is divided by 29 to get 29.

Step 2: Now divide 29 by 29 to get 1. Here, 29 is a prime number that cannot be divided anymore. So, the prime factorization of 841 is: 29 × 29 or 29².

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 841: (1, 841) and (29, 29).

• Negative factor pairs of 841: (-1, -841) and (-29, -29).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 841 are 1, 29, and 841.

• Prime factors: The factors which are prime numbers. For example, 29 is a prime factor of 841.

• 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 841 are (1, 841) and (29, 29).

• Perfect square: A number that is the square of an integer. For example, 841 is a perfect square because it is 29².

• Square root: The number that when multiplied by itself gives the original number. For example, the square root of 841 is 29.