Question

List five multiples of each number $$66$$

Short answer

The first five multiples of 66 are 66, 132, 198, 264, and 330.

Step-by-step solution

- Understand what a multiple is

A multiple of a number is the product of that number and any integer. For example, the multiples of 3 are 3, 6, 9, 12, etc., because those are the results of multiplying 3 with 1, 2, 3, 4, and so on.

- Start with the first multiple

The first multiple of 66 is found by multiplying it with 1: \[ 66 \times 1 = 66 \]So, the first multiple is 66.

- Find the second multiple

The second multiple of 66 is found by multiplying it with 2: \[ 66 \times 2 = 132 \]So, the second multiple is 132.

- Find the third multiple

The third multiple of 66 is found by multiplying it with 3: \[ 66 \times 3 = 198 \]So, the third multiple is 198.

- Find the fourth multiple

The fourth multiple of 66 is found by multiplying it with 4: \[ 66 \times 4 = 264 \]So, the fourth multiple is 264.

- Find the fifth multiple

The fifth multiple of 66 is found by multiplying it with 5: \[ 66 \times 5 = 330 \]So, the fifth multiple is 330.

Key concepts

headline of the respective core concept

To understand the concept of multiples, you need to know about multiplication. Multiplication is one of the basic arithmetic operations. It involves finding the product of two numbers. Think of it as repeated addition. For example, multiplying 3 by 4 is the same as adding 3 four times (3 + 3 + 3 + 3), which is 12.

Multiplication has several properties. It is:

• Commutative: Changing the order of the numbers you multiply does not change the result. For example, 4 × 3 is equal to 3 × 4.
• Associative: Changing the grouping of the numbers you multiply does not change the result. For example, (2 × 3) × 4 is equal to 2 × (3 × 4).
• Distributive: Multiplication distributes over addition. For example, 2 × (3 + 4) is equal to (2 × 3) + (2 × 4).

To find multiples, you multiply the target number by whole numbers (integers). For instance, the multiples of 3 are 3, 6, 9, 12, and so on, found by multiplying 3 by 1, 2, 3, 4, etc.

headline of the respective core concept

Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. So, -3, -2, -1, 0, 1, 2, 3, etc., are all integers.
Integers are important in multiplication because when you multiply any integer by another integer, the result is also an integer.
For example, when you multiply 66 by 1, 2, 3, 4, and 5, the results are all integers (66, 132, 198, 264, and 330).
Understanding integers helps in grasping more complex mathematical concepts. It also aids in solving problems like finding multiples.

• Positive integers are greater than zero (1, 2, 3, ...).
• Negative integers are less than zero (-1, -2, -3, ...).
• Zero is considered an integer, but it is neither positive nor negative.

Knowing how to work with integers makes it easier to perform arithmetic operations and solve related problems.

headline of the respective core concept

Basic arithmetic includes the fundamental operations of addition, subtraction, multiplication, and division. These operations are the building blocks for more complex math concepts.
Here is a quick summary of these operations:

• Addition: Combining two or more numbers to get a total.
• Subtraction: Finding the difference between two numbers.
• Multiplication: Finding the product of two numbers (repeated addition).
• Division: Splitting a number into equal parts.

In the context of finding multiples, we focus on multiplication. Multiples of a number are found by continually adding the number to itself or by multiplying it by the sequence of whole numbers.
For example, the first five multiples of 66 are found as follows:

• First multiple: 66 × 1 = 66
• Second multiple: 66 × 2 = 132
• Third multiple: 66 × 3 = 198
• Fourth multiple: 66 × 4 = 264
• Fifth multiple: 66 × 5 = 330

Understanding these arithmetic operations is crucial in solving a wide range of mathematical problems.