# Multiples of 6

Created by: Team Maths - Examples.com, Last Updated: May 21, 2024

## Multiples of 6

Multiples of 6 are numbers that result from multiplying 6 by any integer. In mathematics, these numbers, such as 6, 12, 18, and 24, are produced by the multiplication process involving 6. Understanding multiples involves recognizing factors and divisors, as a multiple of 6 can be evenly divided by 6 without leaving a remainder. Identifying these multiples is crucial for solving problems related to divisibility and finding common multiples in various mathematical contexts.

## What are Multiples of 6?

Multiples of 6 are numbers that result from multiplying 6 by any integer. These numbers include 6, 12, 18, 24, and so on, continuing indefinitely. Each multiple of 6 is evenly divisible by 6 without any remainder.

Prime factorization of 6: 2 x 3 First 10 multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Table of 6

## What are the multiples and factors of 6?

The multiples of 6 are the numbers you get by multiplying 6 by any whole number: 6, 12, 18, 24, 30, and so on. The factors of 6 are the numbers that divide 6 exactly without leaving a remainder: 1, 2, 3, and 6. In other words, a factor of 6 is any number that can be multiplied by another number to equal 6. For instance, 2 and 3 are factors because 2×3 = 6. Understanding these concepts is crucial for solving various arithmetic problems and simplifying fractions.

## Important Notes

• Multiples of 6: Any number that can be expressed as 6×n, where n is a whole number (e.g., 6, 12, 18, 24).
• Factors of 6: Numbers that divide 6 without leaving a remainder, specifically 1, 2, 3, and 6.
• Prime Factorization of 6: 6 can be expressed as 2×3, both of which are prime numbers.
• Common Uses: Knowing multiples and factors helps in simplifying fractions, solving problems involving divisibility, and finding least common multiples (LCM) and greatest common divisors (GCD).
• Visualization: Creating factor trees or multiplication tables can help visualize and understand the relationship between factors and multiples.

## Examples on Multiples of 6

### Example 1: Identifying Multiples of 6

To find multiples of 6, simply multiply 6 by different whole numbers:

• 6 x 1 = 6
• 6 x 2 = 12
• 6 x 3 = 18
• 6 x 4 = 24
• 6 x 5 = 30

So, the first five multiples of 6 are 6, 12, 18, 24, and 30.

### Example 2: Finding a Multiple of 6 in a Range

Suppose you want to find out if the number 42 is a multiple of 6. To check this, you can divide 42 by 6:

42÷6 = 7

Since 42 divided by 6 equals a whole number (7), this means that 42 is indeed a multiple of 6.

### Example 3: Real-Life Application of Multiples of 6

Imagine you are organizing a party and you want to arrange chairs in rows of 6. If you have 48 chairs, you need to determine if 48 can be evenly distributed into rows of 6:

48÷6 = 8

Since 48 divided by 6 equals a whole number (8), you can arrange the chairs in exactly 8 rows of 6 chairs each. Thus, 48 is a multiple of 6.

## Practical Examples of Multiples of 6

### Example 1: Grouping Students for Activities

Imagine you are a teacher and you want to divide your class of 30 students into smaller groups for a science activity. You decide each group should have 6 students. To check if this arrangement is feasible:

30÷6 = 5

Since 30 divided by 6 equals 5, you can form 5 groups with 6 students each. Therefore, 30 is a multiple of 6.

### Example 2: Packaging Products

A company packages bottles of water in cartons that each hold 6 bottles. If they have 72 bottles to pack, they need to determine how many cartons they will need:

72÷6 = 12

Since 72 divided by 6 equals 12, they will need 12 cartons to pack all the bottles. Hence, 72 is a multiple of 6.

### Example 3: Scheduling Events

Consider a conference organizer who schedules coffee breaks every 6 hours during a 24-hour event. To determine how many breaks will be scheduled:

24÷6 = 4

Since 24 divided by 6 equals 4, there will be 4 coffee breaks in the 24-hour period. Thus, 24 is a multiple of 6.

## What are the first ten multiples of 6?

The first ten multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60.

## How can I determine if a number is a multiple of 6?

A number is a multiple of 6 if it is divisible by both 2 and 3. This means the number must be even and the sum of its digits must be divisible by 3.

## What is the smallest multiple of 6?

The smallest multiple of 6 is 6 itself.

## Are all multiples of 6 also multiples of 3?

Yes, all multiples of 6 are also multiples of 3, since 6 is a product of 2 and 3.

## What is the 15th multiple of 6?

The 15th multiple of 6 is 15×6 = 90.

## How do multiples of 6 appear on a number line?

On a number line, multiples of 6 are evenly spaced at intervals of 6 units. For example, starting from 0, the points will be at 6, 12, 18, and so on.

## Is 72 a multiple of 6? How can you tell?

Yes, 72 is a multiple of 6. It is even (divisible by 2), and the sum of its digits (7 + 2 = 9) is divisible by 3.

## What are common multiples of 6 and 8?

Common multiples of 6 and 8 include 24, 48, 72, and so on. These numbers are multiples of both 6 and 8.

## How are multiples of 6 used in real life?

Multiples of 6 are often used in scenarios involving grouping, packaging, and time calculations, such as organizing items in groups of 6 or determining the time in 6-hour intervals.

## Can a prime number be a multiple of 6?

No, a prime number cannot be a multiple of 6 because prime numbers have exactly two distinct positive divisors: 1 and the number itself. Multiples of 6 have more than two divisors, including 1, 2, 3, and 6.

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