Multiples of 28

Multiples of 28 refer to the numbers obtained by multiplying 28 by various integers. In mathematics, a multiple is a product of a given number and an integer. For instance, 28 multiplied by 1, 2, 3, and so on results in its multiples: 28, 56, 84, etc. These numbers share common divisors and factors, making them integral to understanding number theory and multiplication principles. Identifying multiples of 28 helps in solving problems related to divisors and factors in integer mathematics.

What are Multiples of 28?

Multiples of 28 are the numbers that result from multiplying 28 by any whole number. They follow the pattern 28, 56, 84, 112, and so on. In general, the nth multiple of 28 can be represented as 28n, where n is a positive integer.

Prime Factorization of 28: 28 = 2² × 7 First 10 multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280.

For example, 84, 140, 196 and 252 are all multiples of 28, 501 is not a multiple of 28 for the following reasons:

Number	Calculation	Reason	Remainder
84	84÷28 = 3	84 is a multiple of 28 because it divides evenly.	0
140	140÷28 = 5	140 is a multiple of 28 because it divides evenly.	0
196	196÷28 = 7	196 is a multiple of 28 because it divides evenly.	0
252	252÷28 =9	252 is a multiple of 28 because it divides evenly.	0
501	501÷28 = 17	501 is not a multiple of 28 because it does not divide evenly.	25

List of First 100 Multiples of 28 with Remainders

Number	Reason	Remainder
28	28 is a multiple of 28 because 28 × 1 = 28	0
56	56 is a multiple of 28 because 28 × 2 = 56	0
84	84 is a multiple of 28 because 28 × 3 = 84	0
112	112 is a multiple of 28 because 28 × 4 = 112	0
140	140 is a multiple of 28 because 28 × 5 = 140	0
168	168 is a multiple of 28 because 28 × 6 = 168	0
196	196 is a multiple of 28 because 28 × 7 = 196	0
224	224 is a multiple of 28 because 28 × 8 = 224	0
252	252 is a multiple of 28 because 28 × 9 = 252	0
280	280 is a multiple of 28 because 28 × 10 = 280	0
308	308 is a multiple of 28 because 28 × 11 = 308	0
336	336 is a multiple of 28 because 28 × 12 = 336	0
364	364 is a multiple of 28 because 28 × 13 = 364	0
392	392 is a multiple of 28 because 28 × 14 = 392	0
420	420 is a multiple of 28 because 28 × 15 = 420	0
448	448 is a multiple of 28 because 28 × 16 = 448	0
476	476 is a multiple of 28 because 28 × 17 = 476	0
504	504 is a multiple of 28 because 28 × 18 = 504	0
532	532 is a multiple of 28 because 28 × 19 = 532	0
560	560 is a multiple of 28 because 28 × 20 = 560	0
588	588 is a multiple of 28 because 28 × 21 = 588	0
616	616 is a multiple of 28 because 28 × 22 = 616	0
644	644 is a multiple of 28 because 28 × 23 = 644	0
672	672 is a multiple of 28 because 28 × 24 = 672	0
700	700 is a multiple of 28 because 28 × 25 = 700	0
728	728 is a multiple of 28 because 28 × 26 = 728	0
756	756 is a multiple of 28 because 28 × 27 = 756	0
784	784 is a multiple of 28 because 28 × 28 = 784	0
812	812 is a multiple of 28 because 28 × 29 = 812	0
840	840 is a multiple of 28 because 28 × 30 = 840	0
868	868 is a multiple of 28 because 28 × 31 = 868	0
896	896 is a multiple of 28 because 28 × 32 = 896	0
924	924 is a multiple of 28 because 28 × 33 = 924	0
952	952 is a multiple of 28 because 28 × 34 = 952	0
980	980 is a multiple of 28 because 28 × 35 = 980	0
1008	1008 is a multiple of 28 because 28 × 36 = 1008	0
1036	1036 is a multiple of 28 because 28 × 37 = 1036	0
1064	1064 is a multiple of 28 because 28 × 38 = 1064	0
1092	1092 is a multiple of 28 because 28 × 39 = 1092	0
1120	1120 is a multiple of 28 because 28 × 40 = 1120	0
1148	1148 is a multiple of 28 because 28 × 41 = 1148	0
1176	1176 is a multiple of 28 because 28 × 42 = 1176	0
1204	1204 is a multiple of 28 because 28 × 43 = 1204	0
1232	1232 is a multiple of 28 because 28 × 44 = 1232	0
1260	1260 is a multiple of 28 because 28 × 45 = 1260	0
1288	1288 is a multiple of 28 because 28 × 46 = 1288	0
1316	1316 is a multiple of 28 because 28 × 47 = 1316	0
1344	1344 is a multiple of 28 because 28 × 48 = 1344	0
1372	1372 is a multiple of 28 because 28 × 49 = 1372	0
1400	1400 is a multiple of 28 because 28 × 50 = 1400	0
1428	1428 is a multiple of 28 because 28 × 51 = 1428	0
1456	1456 is a multiple of 28 because 28 × 52 = 1456	0
1484	1484 is a multiple of 28 because 28 × 53 = 1484	0
1512	1512 is a multiple of 28 because 28 × 54 = 1512	0
1540	1540 is a multiple of 28 because 28 × 55 = 1540	0
1568	1568 is a multiple of 28 because 28 × 56 = 1568	0
1596	1596 is a multiple of 28 because 28 × 57 = 1596	0
1624	1624 is a multiple of 28 because 28 × 58 = 1624	0
1652	1652 is a multiple of 28 because 28 × 59 = 1652	0
1680	1680 is a multiple of 28 because 28 × 60 = 1680	0
1708	1708 is a multiple of 28 because 28 × 61 = 1708	0
1736	1736 is a multiple of 28 because 28 × 62 = 1736	0
1764	1764 is a multiple of 28 because 28 × 63 = 1764	0
1792	1792 is a multiple of 28 because 28 × 64 = 1792	0
1820	1820 is a multiple of 28 because 28 × 65 = 1820	0
1848	1848 is a multiple of 28 because 28 × 66 = 1848	0
1876	1876 is a multiple of 28 because 28 × 67 = 1876	0
1904	1904 is a multiple of 28 because 28 × 68 = 1904	0
1932	1932 is a multiple of 28 because 28 × 69 = 1932	0
1960	1960 is a multiple of 28 because 28 × 70 = 1960	0
1988	1988 is a multiple of 28 because 28 × 71 = 1988	0
2016	2016 is a multiple of 28 because 28 × 72 = 2016	0
2044	2044 is a multiple of 28 because 28 × 73 = 2044	0
2072	2072 is a multiple of 28 because 28 × 74 = 2072	0
2100	2100 is a multiple of 28 because 28 × 75 = 2100	0
2128	2128 is a multiple of 28 because 28 × 76 = 2128	0
2156	2156 is a multiple of 28 because 28 × 77 = 2156	0
2184	2184 is a multiple of 28 because 28 × 78 = 2184	0
2212	2212 is a multiple of 28 because 28 × 79 = 2212	0
2240	2240 is a multiple of 28 because 28 × 80 = 2240	0
2268	2268 is a multiple of 28 because 28 × 81 = 2268	0
2296	2296 is a multiple of 28 because 28 × 82 = 2296	0
2324	2324 is a multiple of 28 because 28 × 83 = 2324	0
2352	2352 is a multiple of 28 because 28 × 84 = 2352	0
2380	2380 is a multiple of 28 because 28 × 85 = 2380	0
2408	2408 is a multiple of 28 because 28 × 86 = 2408	0
2436	2436 is a multiple of 28 because 28 × 87 = 2436	0
2464	2464 is a multiple of 28 because 28 × 88 = 2464	0
2492	2492 is a multiple of 28 because 28 × 89 = 2492	0
2520	2520 is a multiple of 28 because 28 × 90 = 2520	0
2548	2548 is a multiple of 28 because 28 × 91 = 2548	0
2576	2576 is a multiple of 28 because 28 × 92 = 2576	0
2604	2604 is a multiple of 28 because 28 × 93 = 2604	0
2632	2632 is a multiple of 28 because 28 × 94 = 2632	0
2660	2660 is a multiple of 28 because 28 × 95 = 2660	0
2688	2688 is a multiple of 28 because 28 × 96 = 2688	0
2716	2716 is a multiple of 28 because 28 × 97 = 2716	0
2744	2744 is a multiple of 28 because 28 × 98 = 2744	0
2772	2772 is a multiple of 28 because 28 × 99 = 2772	0
2800	2800 is a multiple of 28 because 28 × 100 = 2800	0

Read More About Multiples of 28

Table of 28

Important Notes

Step 1: Definition of Multiples

Multiples of a number are the products of that number and any integer. For example, the multiples of 28 are found by multiplying 28 by integers such as 1, 2, 3, etc.

Step 2: First Ten Multiples of 28

The first ten multiples of 28 are:

• 28×1 = 28
• 28×2 = 56
• 28×3 = 84
• 28×4 = 112
• 28×5 = 140
• 28×6 = 168
• 28×7 = 196
• 28×8 = 224
• 28×9 = 252
• 28×10 = 280

Step 3: Common Characteristics

• Even Numbers: All multiples of 28 are even because 28 is an even number.
• Divisibility by 4 and 7: Since 28 is divisible by both 4 and 7, all multiples of 28 are also divisible by 4 and 7.

Step 4: Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that is a multiple of both. For instance, the LCM of 28 and another number can be found using the prime factorization method.

Step 5: Applications

• Mathematics Problems: Multiples are useful in solving problems involving patterns, sequences, and factors.
• Real-Life Scenarios: Understanding multiples can help in scheduling events, distributing items evenly, and more.

Examples on Multiples of 28

Example 1: Finding the Least Common Multiple (LCM)

Problem: Find the LCM of 28 and 35.

List the prime factors of each number:

• 28 = 2 × 2 × 7
• 35 = 5 × 7

Identify the highest power of each prime factor:

• Prime factors: 2, 5, 7
• Highest powers: 222², 515¹, 717¹

Multiply these highest powers:

• LCM = 22²×5¹×7¹
• LCM = 4 × 5 × 7 = 140

The LCM of 28 and 35 is 140.

Example 2: Word Problem Involving Multiples

Problem: Sarah is organizing gift bags. Each bag must contain either 28 or 56 candies. If she has 280 candies, how many bags of each type can she make?

Determine the multiples:

• 28 × 10 = 280 (for bags containing 28 candies)
• 56 × 5 = 280 (for bags containing 56 candies)

Possible combinations:

• She can make 10 bags with 28 candies each, or
• She can make 5 bags with 56 candies each.

Sarah can make 10 bags with 28 candies each or 5 bags with 56 candies each.

Example 3: Practical Application in Scheduling

Problem: A train runs every 28 minutes. If the first train leaves at 6:00 AM, at what times will the train depart within the next 4 hours?

List the multiples of 28 within 240 minutes (4 hours):

• 28, 56, 84, 112, 140, 168, 196, 224

Convert these to time:

• 6:00 AM + 28 minutes = 6:28 AM
• 6:00 AM + 56 minutes = 6:56 AM
• 6:00 AM + 84 minutes = 7:24 AM
• 6:00 AM + 112 minutes = 7:52 AM
• 6:00 AM + 140 minutes = 8:20 AM
• 6:00 AM + 168 minutes = 8:48 AM
• 6:00 AM + 196 minutes = 9:16 AM
• 6:00 AM + 224 minutes = 9:44 AM

The train will depart at 6:28 AM, 6:56 AM, 7:24 AM, 7:52 AM, 8:20 AM, 8:48 AM, 9:16 AM, and 9:44 AM.

Example 4: Divisibility Check

Problem: Is 196 a multiple of 28?

Divide 196 by 28:

• 196÷28 = 7

Since the quotient is a whole number, 196 is a multiple of 28.

Yes, 196 is a multiple of 28.

Example 5: Construction Project

Problem: A contractor needs to purchase packs of tiles, with each pack containing 28 tiles. If the project requires 420 tiles, how many packs are needed?

Divide the total number of tiles by the number of tiles per pack:

420÷28 = 15

The contractor needs 15 packs of tiles.

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