Problem 11 - Basic College Mathematics

Question

List all the factors of each number. $$ 1 $$

Step-by-Step Solution

Answer

The factor of 1 is 1.

Step 1: Understand the concept of factors

Factors of a number are whole numbers that can be multiplied together to produce the original number. For example, for the number 6, 1 and 6 are factors because 1 * 6 = 6, likewise 2 and 3 are factors because 2 * 3 = 6.

Step 2: Identify the factors of 1

The number 1 is unique because it has exactly one factor - itself. Therefore, the only factor of 1 is 1.

Key Concepts

factors

When discussing factors, we're talking about specific whole numbers that can be multiplied together to arrive at another number. For instance, if you're given the number 10, the factors are 1, 2, 5, and 10. This is because:

• 1 x 10 = 10
• 2 x 5 = 10

Factors tell us what numbers can exactly divide into another number without any remainder. They help us understand the building blocks of numbers. Understanding factors is essential because it forms a foundation for simplifying fractions, finding greatest common divisors, and solving real-world problems related to division and grouping.

multiplication

Multiplication plays a crucial role in understanding factors. It's the process of adding a number to itself a certain number of times. For example, 3 multiplied by 4 (3 x 4) means adding 3 four times: 3 + 3 + 3 + 3 = 12. Multiplication is visualized as repeated addition, and it helps us see which numbers combine to form other numbers.
If you need to find the factors of a number, you can use multiplication to check which pairs of numbers result in the original number. For instance, to find factors of 12, you can check the following multiplications:

• 1 x 12 = 12
• 2 x 6 = 12
• 3 x 4 = 12

By understanding multiplication, you'll find it easier to identify the factors of any given number.

whole_numbers

Whole numbers include all positive numbers without fractions or decimals, starting from zero (0, 1, 2, 3, and so on). When we talk about factors, we specifically mean whole numbers. For example, the factors of 8 are 1, 2, 4, and 8—all whole numbers. There is no factor like 2.5 or 3.1 when dealing with factors of whole numbers.
Whole numbers help by making the concept of factors straightforward and easy to understand. Whenever you’re asked to find factors, remember you're looking for those clean, simple, whole numbers that fit perfectly into the target number without leaving a remainder.

• Whole numbers are fundamental in mathematics because they are simple and form the basis for more complex calculations.
• Understanding whole numbers is essential for grasping other mathematical concepts like division, multiplication, and factors.