## 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

## 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

## What are the first five multiples of 21?

The first five multiples of 21 are 21, 42, 63, 84, and 105.

## How can I determine if a number is a multiple of 21?

To determine if a number is a multiple of 21, divide the number by 21. If the quotient is an integer and the remainder is 0, the number is a multiple of 21.

## Is 210 a multiple of 21?

Yes, 210 is a multiple of 21 because 210÷21 = 10, which is an integer.

## What is the 10th multiple of 21?

The 10th multiple of 21 is 21×10 = 210.

## Are all multiples of 21 also multiples of 7 and 3?

Yes, because 21 is 7×3, any multiple of 21 is also a multiple of both 7 and 3.

## How do I find the next multiple of 21 after a given multiple?

To find the next multiple of 21, add 21 to the given multiple. For example, after 84, the next multiple is 84+21 = 105.

## Is 154 a multiple of 21?

No, 154 is not a multiple of 21 because 154÷21 = 7, meaning there is a remainder of 7.

## Can a negative number be a multiple of 21?

Yes, negative numbers can be multiples of 21. For example, -21, -42, and -63 are all multiples of 21.

## What is the smallest multiple of 21 greater than 100?

The smallest multiple of 21 greater than 100 is 105.

## How are multiples of 21 used in real life?

Multiples of 21 can be used in various contexts such as dividing groups evenly, scheduling events, or solving problems in number theory and algebra.