What are all the factors, the prime factorization, and factor pairs of 8?

Factors are the building blocks of numbers and are vital to understanding number properties. With 8 as our illustrative example, we delve into the realm of multiplication and division to uncover the numbers that can be multiplied together to get 8. Unraveling the factors of 8 gives us insights into the structure and properties of this number within the world of mathematics.

Factors of a number are the integers which, when multiplied in pairs, give the original number as a product. For instance, factors of 8 are those numbers that can be evenly divided into 8. Here is a list of the factors of 8 depicted in a tabular format for a better understanding:

• 1 x 8 = 8
• 2 x 4 = 8
• 4 x 2 = 8
• 8 x 1 = 8

To discover the factors of 8, we turn to the division method. Start with the smallest integers and divide 8 by these numbers. If the division results in a whole number without any remainder, then the divisor is considered a factor of 8. For example:

8 ÷ 1 = 8 (Thus, 1 is a factor of 8)

8 ÷ 2 = 4 (Hence, 2 is also a factor of 8)

8 ÷ 4 = 2 (Here, 4 is clearly a factor of 8)

8 ÷ 8 = 1 (Finally, 8 is a factor of itself)

It’s evident that the numbers 1, 2, 4, and 8 are the complete set of factors for the number 8.

Pair factors of 8 are pairs of positive or negative numbers that yield 8 when multiplied together. Both the positive and negative pairs are significant as they highlight the versatility of factors.

Positive Pair Factors	Negative Pair Factors
(1, 8)	(-1, -8)
(2, 4)	(-2, -4)

The prime factorization of 8 involves breaking it down into its prime factors which are 2. Since 8 is a power of 2, its prime factorization is relatively straightforward, as shown in the figure below:

• 8 ÷ 2 = 4
• 4 ÷ 2 = 2
• 2 ÷ 2 = 1

As a result, the prime factorization of 8 is 2 × 2 × 2 or 2³.

Here are some key takeaways about the factors of 8:

• There are four positive factors of 8: 1, 2, 4, and 8.
• The prime factorization of 8 is 2³.
• The pair factors of 8 include both positive pairs (1, 8) and (2, 4), as well as negative pairs (-1, -8) and (-2, -4).
• The sum of all factors of 8 (1 + 2 + 4 + 8) equals 15.

• Exercise 1: List all the factors of 8 that are prime numbers.
• Exercise 2: Can 10 be a factor of 8? Explain why or why not.

• Solution to Exercise 1: The only prime number factor of 8 is 2.
• Solution to Exercise 2: No, 10 cannot be a factor of 8 because dividing 8 by 10 does not result in a whole number.