Multiples of 6

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Created by: Team Maths - Examples.com, Last Updated: July 30, 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

For example, 18, 30, 60 are all multiples of 6, 25 is not a multiple of 6 for the following reasons:

NumberReasonRemainder
1818 is divisible by 60
3030 is divisible by 60
6060 is divisible by 60
2525 divided by 6 gives a remainder of 11

List of First 100 Multiples of 6 with Remainders

List-of-First-100-Multiples-of-6
NumberReasonRemainder
66 is divisible by 60
1212 is divisible by 60
1818 is divisible by 60
2424 is divisible by 60
3030 is divisible by 60
3636 is divisible by 60
4242 is divisible by 60
4848 is divisible by 60
5454 is divisible by 60
6060 is divisible by 60
6666 is divisible by 60
7272 is divisible by 60
7878 is divisible by 60
8484 is divisible by 60
9090 is divisible by 60
9696 is divisible by 60
102102 is divisible by 60
108108 is divisible by 60
114114 is divisible by 60
120120 is divisible by 60
126126 is divisible by 60
132132 is divisible by 60
138138 is divisible by 60
144144 is divisible by 60
150150 is divisible by 60
156156 is divisible by 60
162162 is divisible by 60
168168 is divisible by 60
174174 is divisible by 60
180180 is divisible by 60
186186 is divisible by 60
192192 is divisible by 60
198198 is divisible by 60
204204 is divisible by 60
210210 is divisible by 60
216216 is divisible by 60
222222 is divisible by 60
228228 is divisible by 60
234234 is divisible by 60
240240 is divisible by 60
246246 is divisible by 60
252252 is divisible by 60
258258 is divisible by 60
264264 is divisible by 60
270270 is divisible by 60
276276 is divisible by 60
282282 is divisible by 60
288288 is divisible by 60
294294 is divisible by 60
300300 is divisible by 60
306306 is divisible by 60
312312 is divisible by 60
318318 is divisible by 60
324324 is divisible by 60
330330 is divisible by 60
336336 is divisible by 60
342342 is divisible by 60
348348 is divisible by 60
354354 is divisible by 60
360360 is divisible by 60
366366 is divisible by 60
372372 is divisible by 60
378378 is divisible by 60
384384 is divisible by 60
390390 is divisible by 60
396396 is divisible by 60
402402 is divisible by 60
408408 is divisible by 60
414414 is divisible by 60
420420 is divisible by 60
426426 is divisible by 60
432432 is divisible by 60
438438 is divisible by 60
444444 is divisible by 60
450450 is divisible by 60
456456 is divisible by 60
462462 is divisible by 60
468468 is divisible by 60
474474 is divisible by 60
480480 is divisible by 60
486486 is divisible by 60
492492 is divisible by 60
498498 is divisible by 60
504504 is divisible by 60
510510 is divisible by 60
516516 is divisible by 60
522522 is divisible by 60
528528 is divisible by 60
534534 is divisible by 60
540540 is divisible by 60
546546 is divisible by 60
552552 is divisible by 60
558558 is divisible by 60
564564 is divisible by 60
570570 is divisible by 60
576576 is divisible by 60
582582 is divisible by 60
588588 is divisible by 60
594594 is divisible by 60
600600 is divisible by 60

Read More About Multiples of 6

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.

FAQs

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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