Factors of 104

The numbers that divide 104 evenly are known as factors of 104. A factor of 104 is a number that divides the number without remainder. The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.

Negative factors of 104: -1, -2, -4, -8, -13, -26, -52, and -104.

Prime factors of 104: 2 and 13.

Prime factorization of 104: 2³ × 13.

The sum of factors of 104: 1 + 2 + 4 + 8 + 13 + 26 + 52 + 104 = 210

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 104. Identifying the numbers which are multiplied to get the number 104 is the multiplication method.

Step 1: Multiply 104 by 1, 104 × 1 = 104.

Step 2: Check for other numbers that give 104 after multiplying 2 × 52 = 104

4 × 26 = 104

8 × 13 = 104

Therefore, the positive factor pairs of 104 are: (1, 104), (2, 52), (4, 26), (8, 13). All these factor pairs result in 104. 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 104 by 1, 104 ÷ 1 = 104.

Step 2: Continue dividing 104 by the numbers until the remainder becomes 0.

104 ÷ 1 = 104

104 ÷ 2 = 52

104 ÷ 4 = 26

104 ÷ 8 = 13

Therefore, the factors of 104 are: 1, 2, 4, 8, 13, 26, 52, 104.

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

104 ÷ 2 = 52

52 ÷ 2 = 26

26 ÷ 2 = 13

13 ÷ 13 = 1

The prime factors of 104 are 2 and 13. The prime factorization of 104 is: 2³ × 13.

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

Step 1: Firstly, 104 is divided by 2 to get 52. Step 2: Now divide 52 by 2 to get 26.

Step 3: Then divide 26 by 2 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 104 is: 2³ × 13.

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 104: (1, 104), (2, 52), (4, 26), and (8, 13).
• Negative factor pairs of 104: (-1, -104), (-2, -52), (-4, -26), and (-8, -13).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.

• Prime factors: The factors which are prime numbers. For example, 2 and 13 are prime factors of 104.

• 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 104 are (1, 104), (2, 52), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For 104, it is 2³ × 13.

• Multiple: A number that can be divided by another number without a remainder. For example, 104 is a multiple of 4.