Multiples of 21

Multiples of 21 are the numbers you get when you multiply 21 by any integer. These numbers form a sequence where each term is a product of 21 and an integer, such as 21, 42, 63, and so on. Multiples of 21 are part of basic arithmetic and play a crucial role in understanding concepts like multiplication, factors, and divisors. By identifying these multiples, students can better grasp the relationships between numbers and how they interact through multiplication. Understanding multiples also helps in solving various maths problems related to divisibility and number patterns.

What are Multiples of 21?

Multiples of 21 are numbers obtained by multiplying 21 by any integer. Examples include 21, 42, 63, 84, and so on. These multiples are integral in understanding factors, divisors, and patterns in arithmetic.

Prime factorization of 21: 21 = 3 × 7 First 10 multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210.

For example, 63, 105, 147 and 189 are all multiples of 21, 250 is not a multiple of 21 for the following reasons:

Number	Reason	Remainder
63	63 is a multiple of 21 because 21×3 = 63.	0
105	105 is a multiple of 21 because 21×5 = 105.	0
147	147 is a multiple of 21 because 21×7 = 147.	0
189	189 is a multiple of 21 because 21×9 = 189.	0
250	250 is not a multiple of 21 because 250÷21 = 11.	19

List of First 100 Multiples of 21 with Remainders

Number	Reason	Remainder
21	21 is a multiple of 21 because 21 × 1 = 21	0
42	42 is a multiple of 21 because 21 × 2 = 42	0
63	63 is a multiple of 21 because 21 × 3 = 63	0
84	84 is a multiple of 21 because 21 × 4 = 84	0
105	105 is a multiple of 21 because 21 × 5 = 105	0
126	126 is a multiple of 21 because 21 × 6 = 126	0
147	147 is a multiple of 21 because 21 × 7 = 147	0
168	168 is a multiple of 21 because 21 × 8 = 168	0
189	189 is a multiple of 21 because 21 × 9 = 189	0
210	210 is a multiple of 21 because 21 × 10 = 210	0
231	231 is a multiple of 21 because 21 × 11 = 231	0
252	252 is a multiple of 21 because 21 × 12 = 252	0
273	273 is a multiple of 21 because 21 × 13 = 273	0
294	294 is a multiple of 21 because 21 × 14 = 294	0
315	315 is a multiple of 21 because 21 × 15 = 315	0
336	336 is a multiple of 21 because 21 × 16 = 336	0
357	357 is a multiple of 21 because 21 × 17 = 357	0
378	378 is a multiple of 21 because 21 × 18 = 378	0
399	399 is a multiple of 21 because 21 × 19 = 399	0
420	420 is a multiple of 21 because 21 × 20 = 420	0
441	441 is a multiple of 21 because 21 × 21 = 441	0
462	462 is a multiple of 21 because 21 × 22 = 462	0
483	483 is a multiple of 21 because 21 × 23 = 483	0
504	504 is a multiple of 21 because 21 × 24 = 504	0
525	525 is a multiple of 21 because 21 × 25 = 525	0
546	546 is a multiple of 21 because 21 × 26 = 546	0
567	567 is a multiple of 21 because 21 × 27 = 567	0
588	588 is a multiple of 21 because 21 × 28 = 588	0
609	609 is a multiple of 21 because 21 × 29 = 609	0
630	630 is a multiple of 21 because 21 × 30 = 630	0
651	651 is a multiple of 21 because 21 × 31 = 651	0
672	672 is a multiple of 21 because 21 × 32 = 672	0
693	693 is a multiple of 21 because 21 × 33 = 693	0
714	714 is a multiple of 21 because 21 × 34 = 714	0
735	735 is a multiple of 21 because 21 × 35 = 735	0
756	756 is a multiple of 21 because 21 × 36 = 756	0
777	777 is a multiple of 21 because 21 × 37 = 777	0
798	798 is a multiple of 21 because 21 × 38 = 798	0
819	819 is a multiple of 21 because 21 × 39 = 819	0
840	840 is a multiple of 21 because 21 × 40 = 840	0
861	861 is a multiple of 21 because 21 × 41 = 861	0
882	882 is a multiple of 21 because 21 × 42 = 882	0
903	903 is a multiple of 21 because 21 × 43 = 903	0
924	924 is a multiple of 21 because 21 × 44 = 924	0
945	945 is a multiple of 21 because 21 × 45 = 945	0
966	966 is a multiple of 21 because 21 × 46 = 966	0
987	987 is a multiple of 21 because 21 × 47 = 987	0
1008	1008 is a multiple of 21 because 21 × 48 = 1008	0
1029	1029 is a multiple of 21 because 21 × 49 = 1029	0
1050	1050 is a multiple of 21 because 21 × 50 = 1050	0
1071	1071 is a multiple of 21 because 21 × 51 = 1071	0
1092	1092 is a multiple of 21 because 21 × 52 = 1092	0
1113	1113 is a multiple of 21 because 21 × 53 = 1113	0
1134	1134 is a multiple of 21 because 21 × 54 = 1134	0
1155	1155 is a multiple of 21 because 21 × 55 = 1155	0
1176	1176 is a multiple of 21 because 21 × 56 = 1176	0
1197	1197 is a multiple of 21 because 21 × 57 = 1197	0
1218	1218 is a multiple of 21 because 21 × 58 = 1218	0
1239	1239 is a multiple of 21 because 21 × 59 = 1239	0
1260	1260 is a multiple of 21 because 21 × 60 = 1260	0
1281	1281 is a multiple of 21 because 21 × 61 = 1281	0
1302	1302 is a multiple of 21 because 21 × 62 = 1302	0
1323	1323 is a multiple of 21 because 21 × 63 = 1323	0
1344	1344 is a multiple of 21 because 21 × 64 = 1344	0
1365	1365 is a multiple of 21 because 21 × 65 = 1365	0
1386	1386 is a multiple of 21 because 21 × 66 = 1386	0
1407	1407 is a multiple of 21 because 21 × 67 = 1407	0
1428	1428 is a multiple of 21 because 21 × 68 = 1428	0
1449	1449 is a multiple of 21 because 21 × 69 = 1449	0
1470	1470 is a multiple of 21 because 21 × 70 = 1470	0
1491	1491 is a multiple of 21 because 21 × 71 = 1491	0
1512	1512 is a multiple of 21 because 21 × 72 = 1512	0
1533	1533 is a multiple of 21 because 21 × 73 = 1533	0
1554	1554 is a multiple of 21 because 21 × 74 = 1554	0
1575	1575 is a multiple of 21 because 21 × 75 = 1575	0
1596	1596 is a multiple of 21 because 21 × 76 = 1596	0
1617	1617 is a multiple of 21 because 21 × 77 = 1617	0
1638	1638 is a multiple of 21 because 21 × 78 = 1638	0
1659	1659 is a multiple of 21 because 21 × 79 = 1659	0
1680	1680 is a multiple of 21 because 21 × 80 = 1680	0
1701	1701 is a multiple of 21 because 21 × 81 = 1701	0
1722	1722 is a multiple of 21 because 21 × 82 = 1722	0
1743	1743 is a multiple of 21 because 21 × 83 = 1743	0
1764	1764 is a multiple of 21 because 21 × 84 = 1764	0
1785	1785 is a multiple of 21 because 21 × 85 = 1785	0
1806	1806 is a multiple of 21 because 21 × 86 = 1806	0
1827	1827 is a multiple of 21 because 21 × 87 = 1827	0
1848	1848 is a multiple of 21 because 21 × 88 = 1848	0
1869	1869 is a multiple of 21 because 21 × 89 = 1869	0
1890	1890 is a multiple of 21 because 21 × 90 = 1890	0
1911	1911 is a multiple of 21 because 21 × 91 = 1911	0
1932	1932 is a multiple of 21 because 21 × 92 = 1932	0
1953	1953 is a multiple of 21 because 21 × 93 = 1953	0
1974	1974 is a multiple of 21 because 21 × 94 = 1974	0
1995	1995 is a multiple of 21 because 21 × 95 = 1995	0
2016	2016 is a multiple of 21 because 21 × 96 = 2016	0
2037	2037 is a multiple of 21 because 21 × 97 = 2037	0
2058	2058 is a multiple of 21 because 21 × 98 = 2058	0
2079	2079 is a multiple of 21 because 21 × 99 = 2079	0
2100	2100 is a multiple of 21 because 21 × 100 = 2100	0

Read More About Multiples of 21

Table of 21

Important Notes

Definition: Multiples of 21 are the products of 21 and any integer. In other words, a number n is a multiple of 21 if there exists an integer k such that n = 21×kn.

Identification: To identify if a number is a multiple of 21, divide the number by 21. If the result is an integer with no remainder, the number is a multiple of 21.

First Few Multiples: The first few multiples of 21 are 21, 42, 63, 84, 105, 126, 147, 168, 189, and 210.

Properties:

• Even Distribution: Multiples of 21 are evenly spaced by 21 units.
• Divisibility: A multiple of 21 is always divisible by both 3 and 7, since 21 = 3×7.

Applications:

Common Multiples: Finding common multiples of 21 with other numbers can be useful in solving least common multiple (LCM) problems.

Patterns: Understanding multiples of 21 can help in recognizing numerical patterns and sequences in mathematics.

Examples: For example, 42, 84, and 126 are all multiples of 21 because 21×2 = 42, 21×4 = 84, and 21×6 = 126. Conversely, a number like 100 is not a multiple of 21 because 100÷21 does not result in an integer.

Examples on Multiples of 21

Example 1:

• Calculation: 21×1
• Result: 21
• Explanation: The first multiple of 21 is 21 itself.

Example 2:

• Calculation: 21×4
• Result: 84
• Explanation: Multiply 21 by 4 to get the fourth multiple of 21, which is 84.

Example 3:

• Calculation: 21×7
• Result: 147
• Explanation: Multiply 21 by 7 to get the seventh multiple of 21, which is 147.

Example 4:

• Calculation: 21×10
• Result: 210
• Explanation: Multiply 21 by 10 to get the tenth multiple of 21, which is 210.

Example 5:

• Calculation: 21×12
• Result: 252
• Explanation: Multiply 21 by 12 to get the twelfth multiple of 21, which is 252.

Verification of Multiples

To verify if a number is a multiple of 21, divide the number by 21 and check if the remainder is zero.

Example 6:

• Number: 189
• Calculation: 189÷21 = 9
• Remainder: 0
• Explanation: Since the remainder is 0, 189 is a multiple of 21.

Example 7:

• Number: 250
• Calculation: 250÷21 = 11
• Remainder: 19
• Explanation: Since the remainder is 19, 250 is not a multiple of 21.

FAQs