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:

Number	Reason	Remainder
18	18 is divisible by 6	0
30	30 is divisible by 6	0
60	60 is divisible by 6	0
25	25 divided by 6 gives a remainder of 1	1

List of First 100 Multiples of 6 with Remainders

Number	Reason	Remainder
6	6 is divisible by 6	0
12	12 is divisible by 6	0
18	18 is divisible by 6	0
24	24 is divisible by 6	0
30	30 is divisible by 6	0
36	36 is divisible by 6	0
42	42 is divisible by 6	0
48	48 is divisible by 6	0
54	54 is divisible by 6	0
60	60 is divisible by 6	0
66	66 is divisible by 6	0
72	72 is divisible by 6	0
78	78 is divisible by 6	0
84	84 is divisible by 6	0
90	90 is divisible by 6	0
96	96 is divisible by 6	0
102	102 is divisible by 6	0
108	108 is divisible by 6	0
114	114 is divisible by 6	0
120	120 is divisible by 6	0
126	126 is divisible by 6	0
132	132 is divisible by 6	0
138	138 is divisible by 6	0
144	144 is divisible by 6	0
150	150 is divisible by 6	0
156	156 is divisible by 6	0
162	162 is divisible by 6	0
168	168 is divisible by 6	0
174	174 is divisible by 6	0
180	180 is divisible by 6	0
186	186 is divisible by 6	0
192	192 is divisible by 6	0
198	198 is divisible by 6	0
204	204 is divisible by 6	0
210	210 is divisible by 6	0
216	216 is divisible by 6	0
222	222 is divisible by 6	0
228	228 is divisible by 6	0
234	234 is divisible by 6	0
240	240 is divisible by 6	0
246	246 is divisible by 6	0
252	252 is divisible by 6	0
258	258 is divisible by 6	0
264	264 is divisible by 6	0
270	270 is divisible by 6	0
276	276 is divisible by 6	0
282	282 is divisible by 6	0
288	288 is divisible by 6	0
294	294 is divisible by 6	0
300	300 is divisible by 6	0
306	306 is divisible by 6	0
312	312 is divisible by 6	0
318	318 is divisible by 6	0
324	324 is divisible by 6	0
330	330 is divisible by 6	0
336	336 is divisible by 6	0
342	342 is divisible by 6	0
348	348 is divisible by 6	0
354	354 is divisible by 6	0
360	360 is divisible by 6	0
366	366 is divisible by 6	0
372	372 is divisible by 6	0
378	378 is divisible by 6	0
384	384 is divisible by 6	0
390	390 is divisible by 6	0
396	396 is divisible by 6	0
402	402 is divisible by 6	0
408	408 is divisible by 6	0
414	414 is divisible by 6	0
420	420 is divisible by 6	0
426	426 is divisible by 6	0
432	432 is divisible by 6	0
438	438 is divisible by 6	0
444	444 is divisible by 6	0
450	450 is divisible by 6	0
456	456 is divisible by 6	0
462	462 is divisible by 6	0
468	468 is divisible by 6	0
474	474 is divisible by 6	0
480	480 is divisible by 6	0
486	486 is divisible by 6	0
492	492 is divisible by 6	0
498	498 is divisible by 6	0
504	504 is divisible by 6	0
510	510 is divisible by 6	0
516	516 is divisible by 6	0
522	522 is divisible by 6	0
528	528 is divisible by 6	0
534	534 is divisible by 6	0
540	540 is divisible by 6	0
546	546 is divisible by 6	0
552	552 is divisible by 6	0
558	558 is divisible by 6	0
564	564 is divisible by 6	0
570	570 is divisible by 6	0
576	576 is divisible by 6	0
582	582 is divisible by 6	0
588	588 is divisible by 6	0
594	594 is divisible by 6	0
600	600 is divisible by 6	0

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.

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