The factors of 96 are:

• 1
• 2
• 3
• 4
• 6
• 8
• 12
• 16
• 24
• 32
• 48
• 96

To understand the factors of 96, let's first clarify what a factor is. A factor is a whole number that can be divided evenly into another number without leaving a remainder. In the case of 96, the factors you listed—1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96—are all the numbers that can divide 96 evenly.

Breaking Down the Number 96

To find the factors of 96, we can start by performing a prime factorization. This means we break down 96 into its prime components. The process looks like this:

• 96 is even, so we can divide by 2: 96 ÷ 2 = 48
• 48 is also even: 48 ÷ 2 = 24
• 24 is even: 24 ÷ 2 = 12
• 12 is even: 12 ÷ 2 = 6
• 6 is even: 6 ÷ 2 = 3
• 3 is a prime number and cannot be divided further.

So, the prime factorization of 96 is 2^5 × 3^1. This means that 96 can be expressed as the product of five 2s and one 3.

Finding All Factors

Now, to find all the factors of 96, we can use the prime factorization. Each factor can be formed by taking different combinations of these prime factors. Here’s how we can do that:

• Start with the lowest powers of the prime factors: 2^0 × 3^0 = 1
• Next, include one 2: 2^1 × 3^0 = 2
• Then, include two 2s: 2^2 × 3^0 = 4
• Continue this process until you reach the maximum powers: 2^5 × 3^1 = 96

By systematically combining these factors, we can list all the factors of 96:

• 1
• 2
• 3
• 4
• 6
• 8
• 12
• 16
• 24
• 32
• 48
• 96

Understanding Factor Pairs

Another interesting aspect of factors is that they come in pairs. For example, if you take 1 and 96, they multiply to give 96. Similarly, 2 and 48, 3 and 32, and so on. This pairing can help visualize how factors relate to one another. For instance:

• 1 × 96 = 96
• 2 × 48 = 96
• 3 × 32 = 96
• 4 × 24 = 96
• 6 × 16 = 96
• 8 × 12 = 96

In summary, the factors of 96 are all the numbers that can divide it evenly, and they can be found through prime factorization and combination of those factors. Understanding how to find and pair factors is a valuable skill in mathematics, as it lays the groundwork for more complex concepts like divisibility and prime numbers.