What are all the factors, the prime factorization, and factor pairs of 16?

Factors are numbers that we multiply together to get another number. With 16 as our illustrative example, understanding factors illuminates the structure and properties of 16 within the realm of mathematics. Factors give us insights into divisibility, simplify fractions, and help solve various algebraic problems.

The factors of 16 are the whole numbers that can be multiplied in pairs to give the product as 16. Observing these factors helps us understand number relationships and arithmetic operations involving 16. Here is a list of the factors of 16:

• 1
• 2
• 4
• 8
• 16

To identify the factors of 16, we can employ the division method. This method involves dividing 16 by smaller integers to determine which ones result in a whole number quotient, signaling that the divisor is a factor of 16. Here’s an example:

• 16 ÷ 1 = 16
• 16 ÷ 2 = 8
• 16 ÷ 4 = 4
• 16 ÷ 8 = 2
• 16 ÷ 16 = 1

This process reveals all the factors of 16, which are 1, 2, 4, 8, and 16.

The concept of pair factors refers to two numbers that, when multiplied together, yield 16. Here are the positive and negative pair factors of 16:

The prime factorization of 16 involves breaking down the number into its prime number factors. For 16, the process involves continual division by the prime number 2:

16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

Hence, the prime factors of 16 are 2 × 2 × 2 × 2 or 2⁴.

Some important points about the number 16 and its factors include:

• Total factors of 16: 1, 2, 4, 8, 16.
• Prime factorization of 16: 2⁴.
• Sum of all factors of 16: 1 + 2 + 4 + 8 + 16 = 31.
• 16 is a power of 2, which makes it a perfect square.

1. List all factors of 16.
2. What does the prime factorization of 16 tell us about the number?

1. The factors of 16 are 1, 2, 4, 8, and 16.
2. The prime factorization of 16 is 2⁴, which shows that 16 is a power of 2 and emphasizes its characteristics as a perfect square.