Multiples of 42
Multiples of 42
In mathematics, multiples of 42 are the products obtained by multiplying the integer 42 with other integers. These numbers form a sequence where each term is a result of 42 times a whole number. Understanding multiples is essential in various mathematical concepts, such as finding common multiples, divisors, and factors. Multiples of 42 help in solving problems related to number theory and arithmetic operations. Identifying these multiples can aid in simplifying complex multiplication and division problems.
What are Multiples of 42?
Multiples of 42 are the numbers you get when you multiply 42 by integers. These include 42, 84, 126, 168, 210, and so on. Essentially, any number that can be expressed as 42n, where n is an integer, is a multiple of 42.
For example, 168, 294, 336 and 378 are all multiples of 42, 473 is not a multiple of 42 for the following reasons:
| Number | Calculation | Reason | Remainder |
|---|---|---|---|
| 168 | 168÷42 = 4 | 168 is a multiple of 42 because it divides evenly. | 0 |
| 294 | 294÷42 = 7 | 294 is a multiple of 42 because it divides evenly. | 0 |
| 336 | 336÷42 = 8 | 336 is a multiple of 42 because it divides evenly. | 0 |
| 378 | 378÷42 = 9 | 378 is a multiple of 42 because it divides evenly. | 0 |
| 473 | 473÷42 = 11 | 473 is not a multiple of 42 because it does not divide evenly. | 11 |
List of First 100 Multiples of 42 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 42 | 42 is a multiple of 42 because 42 × 1 = 42 | 0 |
| 84 | 84 is a multiple of 42 because 42 × 2 = 84 | 0 |
| 126 | 126 is a multiple of 42 because 42 × 3 = 126 | 0 |
| 168 | 168 is a multiple of 42 because 42 × 4 = 168 | 0 |
| 210 | 210 is a multiple of 42 because 42 × 5 = 210 | 0 |
| 252 | 252 is a multiple of 42 because 42 × 6 = 252 | 0 |
| 294 | 294 is a multiple of 42 because 42 × 7 = 294 | 0 |
| 336 | 336 is a multiple of 42 because 42 × 8 = 336 | 0 |
| 378 | 378 is a multiple of 42 because 42 × 9 = 378 | 0 |
| 420 | 420 is a multiple of 42 because 42 × 10 = 420 | 0 |
| 462 | 462 is a multiple of 42 because 42 × 11 = 462 | 0 |
| 504 | 504 is a multiple of 42 because 42 × 12 = 504 | 0 |
| 546 | 546 is a multiple of 42 because 42 × 13 = 546 | 0 |
| 588 | 588 is a multiple of 42 because 42 × 14 = 588 | 0 |
| 630 | 630 is a multiple of 42 because 42 × 15 = 630 | 0 |
| 672 | 672 is a multiple of 42 because 42 × 16 = 672 | 0 |
| 714 | 714 is a multiple of 42 because 42 × 17 = 714 | 0 |
| 756 | 756 is a multiple of 42 because 42 × 18 = 756 | 0 |
| 798 | 798 is a multiple of 42 because 42 × 19 = 798 | 0 |
| 840 | 840 is a multiple of 42 because 42 × 20 = 840 | 0 |
| 882 | 882 is a multiple of 42 because 42 × 21 = 882 | 0 |
| 924 | 924 is a multiple of 42 because 42 × 22 = 924 | 0 |
| 966 | 966 is a multiple of 42 because 42 × 23 = 966 | 0 |
| 1008 | 1008 is a multiple of 42 because 42 × 24 = 1008 | 0 |
| 1050 | 1050 is a multiple of 42 because 42 × 25 = 1050 | 0 |
| 1092 | 1092 is a multiple of 42 because 42 × 26 = 1092 | 0 |
| 1134 | 1134 is a multiple of 42 because 42 × 27 = 1134 | 0 |
| 1176 | 1176 is a multiple of 42 because 42 × 28 = 1176 | 0 |
| 1218 | 1218 is a multiple of 42 because 42 × 29 = 1218 | 0 |
| 1260 | 1260 is a multiple of 42 because 42 × 30 = 1260 | 0 |
| 1302 | 1302 is a multiple of 42 because 42 × 31 = 1302 | 0 |
| 1344 | 1344 is a multiple of 42 because 42 × 32 = 1344 | 0 |
| 1386 | 1386 is a multiple of 42 because 42 × 33 = 1386 | 0 |
| 1428 | 1428 is a multiple of 42 because 42 × 34 = 1428 | 0 |
| 1470 | 1470 is a multiple of 42 because 42 × 35 = 1470 | 0 |
| 1512 | 1512 is a multiple of 42 because 42 × 36 = 1512 | 0 |
| 1554 | 1554 is a multiple of 42 because 42 × 37 = 1554 | 0 |
| 1596 | 1596 is a multiple of 42 because 42 × 38 = 1596 | 0 |
| 1638 | 1638 is a multiple of 42 because 42 × 39 = 1638 | 0 |
| 1680 | 1680 is a multiple of 42 because 42 × 40 = 1680 | 0 |
| 1722 | 1722 is a multiple of 42 because 42 × 41 = 1722 | 0 |
| 1764 | 1764 is a multiple of 42 because 42 × 42 = 1764 | 0 |
| 1806 | 1806 is a multiple of 42 because 42 × 43 = 1806 | 0 |
| 1848 | 1848 is a multiple of 42 because 42 × 44 = 1848 | 0 |
| 1890 | 1890 is a multiple of 42 because 42 × 45 = 1890 | 0 |
| 1932 | 1932 is a multiple of 42 because 42 × 46 = 1932 | 0 |
| 1974 | 1974 is a multiple of 42 because 42 × 47 = 1974 | 0 |
| 2016 | 2016 is a multiple of 42 because 42 × 48 = 2016 | 0 |
| 2058 | 2058 is a multiple of 42 because 42 × 49 = 2058 | 0 |
| 2100 | 2100 is a multiple of 42 because 42 × 50 = 2100 | 0 |
| 2142 | 2142 is a multiple of 42 because 42 × 51 = 2142 | 0 |
| 2184 | 2184 is a multiple of 42 because 42 × 52 = 2184 | 0 |
| 2226 | 2226 is a multiple of 42 because 42 × 53 = 2226 | 0 |
| 2268 | 2268 is a multiple of 42 because 42 × 54 = 2268 | 0 |
| 2310 | 2310 is a multiple of 42 because 42 × 55 = 2310 | 0 |
| 2352 | 2352 is a multiple of 42 because 42 × 56 = 2352 | 0 |
| 2394 | 2394 is a multiple of 42 because 42 × 57 = 2394 | 0 |
| 2436 | 2436 is a multiple of 42 because 42 × 58 = 2436 | 0 |
| 2478 | 2478 is a multiple of 42 because 42 × 59 = 2478 | 0 |
| 2520 | 2520 is a multiple of 42 because 42 × 60 = 2520 | 0 |
| 2562 | 2562 is a multiple of 42 because 42 × 61 = 2562 | 0 |
| 2604 | 2604 is a multiple of 42 because 42 × 62 = 2604 | 0 |
| 2646 | 2646 is a multiple of 42 because 42 × 63 = 2646 | 0 |
| 2688 | 2688 is a multiple of 42 because 42 × 64 = 2688 | 0 |
| 2730 | 2730 is a multiple of 42 because 42 × 65 = 2730 | 0 |
| 2772 | 2772 is a multiple of 42 because 42 × 66 = 2772 | 0 |
| 2814 | 2814 is a multiple of 42 because 42 × 67 = 2814 | 0 |
| 2856 | 2856 is a multiple of 42 because 42 × 68 = 2856 | 0 |
| 2898 | 2898 is a multiple of 42 because 42 × 69 = 2898 | 0 |
| 2940 | 2940 is a multiple of 42 because 42 × 70 = 2940 | 0 |
| 2982 | 2982 is a multiple of 42 because 42 × 71 = 2982 | 0 |
| 3024 | 3024 is a multiple of 42 because 42 × 72 = 3024 | 0 |
| 3066 | 3066 is a multiple of 42 because 42 × 73 = 3066 | 0 |
| 3108 | 3108 is a multiple of 42 because 42 × 74 = 3108 | 0 |
| 3150 | 3150 is a multiple of 42 because 42 × 75 = 3150 | 0 |
| 3192 | 3192 is a multiple of 42 because 42 × 76 = 3192 | 0 |
| 3234 | 3234 is a multiple of 42 because 42 × 77 = 3234 | 0 |
| 3276 | 3276 is a multiple of 42 because 42 × 78 = 3276 | 0 |
| 3318 | 3318 is a multiple of 42 because 42 × 79 = 3318 | 0 |
| 3360 | 3360 is a multiple of 42 because 42 × 80 = 3360 | 0 |
| 3402 | 3402 is a multiple of 42 because 42 × 81 = 3402 | 0 |
| 3444 | 3444 is a multiple of 42 because 42 × 82 = 3444 | 0 |
| 3486 | 3486 is a multiple of 42 because 42 × 83 = 3486 | 0 |
| 3528 | 3528 is a multiple of 42 because 42 × 84 = 3528 | 0 |
| 3570 | 3570 is a multiple of 42 because 42 × 85 = 3570 | 0 |
| 3612 | 3612 is a multiple of 42 because 42 × 86 = 3612 | 0 |
| 3654 | 3654 is a multiple of 42 because 42 × 87 = 3654 | 0 |
| 3696 | 3696 is a multiple of 42 because 42 × 88 = 3696 | 0 |
| 3738 | 3738 is a multiple of 42 because 42 × 89 = 3738 | 0 |
| 3780 | 3780 is a multiple of 42 because 42 × 90 = 3780 | 0 |
| 3822 | 3822 is a multiple of 42 because 42 × 91 = 3822 | 0 |
| 3864 | 3864 is a multiple of 42 because 42 × 92 = 3864 | 0 |
| 3906 | 3906 is a multiple of 42 because 42 × 93 = 3906 | 0 |
| 3948 | 3948 is a multiple of 42 because 42 × 94 = 3948 | 0 |
| 3990 | 3990 is a multiple of 42 because 42 × 95 = 3990 | 0 |
| 4032 | 4032 is a multiple of 42 because 42 × 96 = 4032 | 0 |
| 4074 | 4074 is a multiple of 42 because 42 × 97 = 4074 | 0 |
| 4116 | 4116 is a multiple of 42 because 42 × 98 = 4116 | 0 |
| 4158 | 4158 is a multiple of 42 because 42 × 99 = 4158 | 0 |
| 4200 | 4200 is a multiple of 42 because 42 × 100 = 4200 | 0 |
Read More About Multiples of 42
Important Notes
- Definition: Multiples of 42 are numbers that can be expressed as 42n, where n is any integer. Examples include 42, 84, 126, and so on.
- Divisibility: Every multiple of 42 is divisible by both 6 and 7 since 42 is the product of these numbers (42 = 6 × 7).
- Even Nature: All multiples of 42 are even numbers because 42 is an even number.
- Arithmetic Progression: The sequence of multiples of 42 forms an arithmetic progression with the first term being 42 and the common difference also being 42 (e.g., 42, 84, 126, 168).
- Common Multiples: Multiples of 42 can also be multiples of other numbers, especially those that are factors of 42, such as 2, 3, 6, 7, and 21.
Examples on Multiples of 42
Simple Multiples
- 42×1 = 42
- 42×2 = 84
- 42×3 = 126
Larger Multiples
- 42×10 = 420
- 42×20 = 840
- 42×30 = 1260
Real-Life Examples
- Weeks in a Year: There are 52 weeks in a year, which is not a multiple of 42, but considering every 6 weeks and adding one week gives us 42 days, aligning with 6 weeks. Therefore, 42 days (6 weeks) is a useful multiple in planning and scheduling.
- Event Planning: For a conference occurring every 42 days, the pattern helps in organizing recurring events (42 days = 1 cycle, thus 84 days = 2 cycles, etc.).
Practical Examples of Multiples of 42
What is the 15th multiple of 42?
The 15th multiple of 42 is 42×15 = 630.
Is 378 a multiple of 42?
Yes, 378 is a multiple of 42 because 42×9 = 378.
What is the next multiple of 42 after 420?
The next multiple of 42 after 420 is 420+42 = 462.
Find the 25th multiple of 42.
The 25th multiple of 42 is 42×25 = 1050.
Is 1001 a multiple of 42?
No, 1001 is not a multiple of 42 because 1001 cannot be expressed as 42×n for any integer n.
FAQs
What are multiples of 42?
Multiples of 42 are numbers obtained by multiplying 42 by any integer. Examples include 42, 84, 126, 168, and so on.
How can you determine if a number is a multiple of 42?
To determine if a number is a multiple of 42, divide the number by 42. If the result is an integer without a remainder, the number is a multiple of 42.
What is the first multiple of 42?
The first multiple of 42 is 42 itself, as it is 42 multiplied by 1.
Are all multiples of 42 even numbers?
Yes, all multiples of 42 are even numbers because 42 is an even number, and the product of an even number and any integer is always even.
What are the first five multiples of 42?
The first five multiples of 42 are 42, 84, 126, 168, and 210.
How are multiples of 42 related to factors and divisors?
Multiples of 42 share 42 as a common factor. Therefore, 42 is a divisor of all its multiples.
What is the least common multiple (LCM) of 42 and another number?
The least common multiple of 42 and another number is the smallest number that is a multiple of both 42 and the other number. To find it, you can use the prime factorization method.
How do multiples of 42 relate to multiplication tables?
Multiples of 42 can be found in the 42 times table, where each entry is the product of 42 and a counting number (e.g., 42 × 1, 42 × 2).
Can negative numbers be multiples of 42?
Yes, negative numbers can be multiples of 42. For example, -42, -84, and -126 are all multiples of 42.
What is the 10th multiple of 42?
The 10th multiple of 42 is 420, as it is obtained by multiplying 42 by 10 (42 × 10).
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