What are all the factors, the prime factorization, and factor pairs of 64?

Factors are integral components of mathematics that allow us to dissect numbers into smaller, more manageable parts. Like a recipe made up of different ingredients, factors are the numbers we multiply together to get a certain product. For illustrative example, let’s explore the number 64. Understanding the factors of 64 offers a window into the number’s structure and unveils its mathematical significance.

The concept of factors for the number 64 refers to all of the whole numbers that can be multiplied together to reach the product of 64. This includes both the number itself and 1, as every number is divisible by 1 and itself. Below is a visual representation of factors and their pairings as seen in the multiplication process for 64:

• 1 × 64 = 64
• 2 × 32 = 64
• 4 × 16 = 64
• 8 × 8 = 64

Discovering the factors of 64 can be an engaging exercise that illustrates the mathematical divisibility characteristic of integers. We can use the division method to determine which whole numbers divide 64 evenly, leaving no remainder. Below is a step-by-step example:

• 1 is always a factor, so 64 ÷ 1 = 64.
• Continuing with even numbers, 64 is divisible by 2, yielding 64 ÷ 2 = 32.
• Proceeding further, 64 ÷ 4 = 16, so 4 is also a factor.
• The square root of 64 is 8, meaning 64 ÷ 8 = 8.

By systematically dividing 64 by these integers, we confirm that the factors are 1, 2, 4, 8, 16, 32, and 64.

Pair factors of 64 are twofold numbers that, when multiplied together, result in the number 64. For a comprehensive viewpoint, both positive and negative pair factors are enumerated. The following list details these factor pairs:

To further analyze 64, we delve into prime factorization, breaking it down to its prime number multipliers. Here we explain and visually demonstrate this process:

The prime factors of 64 are arrived at by continually dividing it by the smallest prime number, with the process halting once the quotient is 1. For 64, this results in 2 × 2 × 2 × 2 × 2 × 2 or 2⁶, with 2 being the sole prime factor.

• The total number of factors for 64 is 7.
• The prime factor of 64 is 2.
• Pair factors of 64 are (1, 64), (2, 32), (4, 16), and (8, 8).
• The sum of all factors of 64 is 127.
• An interesting fact: 64 is a perfect square, as 8 × 8 = 64.

• Q1: Name a factor of 64 that is greater than 8.
• Q2: If you partition 64 into 4 equal parts, what is the value of each part?
• Q3: How many total prime factors does 64 have?

• A1: A factor of 64 that is greater than 8 is 16.
• A2: Partitioning 64 into 4 equal parts gives each part a value of 16.
• A3: 64 has a total of 6 prime factors, all of which are the number 2.