Problem 28 - Elementary Algebra

Question

For the following problems, specify all the whole number factors of each number. For example, the complete set of whole number factors of 6 is 1,2,3,6 . 2

Step-by-Step Solution

Answer

Answer: The whole number factors of 2 are 1 and 2.

Step 1: Understand the concept of factors

Whole number factors are numbers that can be evenly divided into a given number with no remainder. For example, the factors of 6 are 1, 2, 3, and 6 because 1x6=6 and 2x3=6.

Step 2: Identify the factors of the given number (2)

There are only two whole numbers that can multiply together to form the given number, 2. They are 1 and 2, as 1x2=2 and there are no more possible combinations.

Step 3: Present the solution

The complete set of whole number factors of 2 is 1 and 2.

Key Concepts

Factors

Factors are an essential part of understanding numbers and their properties. When we talk about factors, we mean the numbers that evenly divide another number, leaving no remainder. For example, the factors of 6 are 1, 2, 3, and 6, because:

• 1 multiplied by 6 gives 6, and
• 2 multiplied by 3 gives 6

These computations show the pairs that, when multiplied, yield the original number. This helps us see the combinations of numbers that relate to each other through multiplication. Recognizing factors is beneficial when solving mathematical problems involving division and simplifying fractions.

Divisibility

Divisibility is a vital concept when identifying factors. A number is said to be divisible by another if you can divide it without leaving any remainder. This property is what helps determine the factors of a number. For instance, if we take the number 2:

• When 2 is divided by 1, it leaves no remainder, which makes 1 a factor of 2.
• Also, dividing 2 by itself, which is 2, leaves no remainder, making 2 a factor as well.

This demonstrates that understanding divisibility enables us to find factors effectively. It is particularly useful for simplifying calculations and breaking down complex problems into simpler parts.

Multiplication

Multiplication plays a crucial role in the concept of factors. It is the opposite operation of division. When two whole numbers multiply to produce another number, those numbers are considered factors of the resulting product. For example:

• In the expression 1 x 2 = 2, both 1 and 2 are factors of 2.

This pairing of numbers illustrates how multiplication is a fundamental operation for identifying factors. It can be used in various mathematical operations to check results or to further explore numerical relationships.

Number Properties

Understanding number properties is essential when discussing factors. These properties reveal characteristics and patterns in numbers that are helpful for solving mathematical challenges. Key properties related to factors include:

• Every whole number is a factor of itself.
• The number 1 is a factor of every number.

For example, for the number 2, its properties tell us:

• 2 is a factor because it is the number itself.
• 1 is a factor because every number is divisible by 1 without a remainder.

These properties offer a structured way of understanding factors, which can simplify mathematics problems and enhance number sense. Recognizing these basic properties helps develop a deeper comprehension of how numbers work together.