What are all the factors, the prime factorization, and factor pairs of 96?

Factors of a number are the building blocks that multiply together to create the number itself. Using 96 as an illustrative example, factors are integral numbers that divide 96 without any remainder. Understanding factors is essential as they help in uncovering the structure and mathematical properties of 96, revealing its behavior in various arithmetic operations.

The concept of factors for a number like 96 refers to numbers that can be multiplied in pairs to result in the number itself. A visual representation of this concept is illustrated with a table of pair factors which showcases how different combinations of two numbers can be multiplied to get 96.

To find the factors of 96, we apply the division method. This involves dividing 96 by all integers less than or equal to it to identify which ones result in whole numbers as their quotient; these integers are factors. The process looks like the following:

• 96 ÷ 1 = 96, thus 1 is a factor
• 96 ÷ 2 = 48, thus 2 is a factor

Pair factors of 96 include two numbers that, when multiplied together, result in 96. Below is a table displaying both positive and negative pairs:

The prime factorization of 96 involves breaking it down into its prime factors – the smallest prime numbers that multiply to make 96. Using a factor tree, we can visually decompose 96 into the following prime factors:

Prime Factorization: 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2^5 × 3

• 96 has a total of [total number of factors] factors including 1 and 96 itself.
• The prime factors of 96 are 2 and 3.
• The pair factors of 96 include both positive and negative number combinations.
• The sum of all the factors of 96 is [sum of factors].

Understanding the factors of 96 can be a fun exercise. Try the following questions to test your knowledge:

Below are the solutions to the previously mentioned exercises. Check your answers and understand the concept: