What are all the factors, the prime factorization, and factor pairs of 5?

Factors are the building blocks of numbers that, when multiplied together, result in a product. In the case of the number 5, the factors elucidate its simpleness and its use in various mathematical contexts. Understanding the factors of a number, such as 5, is crucial as it lays the groundwork for advanced mathematical concepts including divisibility, multiples, and prime factorization.

The factors of a number are the integers that divide the number without leaving a remainder. In the case of 5, it has a very exclusive set of factors. Below, we see a visual representation of pairing factors and a complete list demonstrating the simplicity of the number 5.

• 1 × 5 = 5
• 5 × 1 = 5

Thus, the factors of 5 are 1 and 5.

To find the factors of 5, we use the division method. The factors of a number like 5 will be equal to or less than 5. Thus, we divide 5 by smaller integers to check for factors. The division looks as follows:

• 5 ÷ 1 = 5
• 5 ÷ 5 = 1

All other divisions will result in a fractional number, which indicates that 1 and 5 are the only factors of 5.

Pair factors are two numbers that, when multiplied, equal the product 5. For 5, the process is straightforward:

• 1 × 5 = 5

1 and 5 are the only positive pair factors of 5. As for negative pair factors:

• -1 × -5 = 5

Thus, the negative pair factors are (-1, -5).

Since 5 is a prime number, its prime factorization is simple. The prime factor of 5 is 5 itself, represented as 5¹. There is no need for a factor tree as 5 is not composite and does not have factors other than 1 and itself.

Here are some key points about the factors of 5:

• The number 5 has only two factors: 1 and 5.
• 5 is a prime number.
• The prime factorization of 5 is simply 5¹.

Understanding the factors of 5 is fundamental to its role as a building block within the number system, particularly its role in creating multiples and identifying divisibility.

Test your understanding of the factors of 5 with the following questions:

• Is the number 10 a factor of 5?
• Can 5 be divided into two parts that are equal whole numbers?
• What multiplication sentence can you write for the factors of 5?

Here are the solutions to the exercises on the factors of 5:

• No, 10 is not a factor of 5, but rather a multiple.
• No, 5 is a prime number and can only be divided by 1 and itself without leaving a remainder.
• The multiplication sentence for the factors of 5 is 1 × 5 = 5.