Multiples of 42

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Created by: Team Maths - Examples.com, Last Updated: August 21, 2024

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.

Prime Factorization of 42: 2 × 3 × 7 First 10 Multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420.

For example, 168, 294, 336 and 378 are all multiples of 42, 473 is not a multiple of 42 for the following reasons:

NumberCalculationReasonRemainder
168168÷42 = 4168 is a multiple of 42 because it divides evenly.0
294294÷42 = 7294 is a multiple of 42 because it divides evenly.0
336336÷42 = 8336 is a multiple of 42 because it divides evenly.0
378378÷42 = 9378 is a multiple of 42 because it divides evenly.0
473473÷42 = 11473 is not a multiple of 42 because it does not divide evenly.11

List of First 100 Multiples of 42 with Remainders

List-of-First-100-Multiples-of-42
NumberReasonRemainder
4242 is a multiple of 42 because 42 × 1 = 420
8484 is a multiple of 42 because 42 × 2 = 840
126126 is a multiple of 42 because 42 × 3 = 1260
168168 is a multiple of 42 because 42 × 4 = 1680
210210 is a multiple of 42 because 42 × 5 = 2100
252252 is a multiple of 42 because 42 × 6 = 2520
294294 is a multiple of 42 because 42 × 7 = 2940
336336 is a multiple of 42 because 42 × 8 = 3360
378378 is a multiple of 42 because 42 × 9 = 3780
420420 is a multiple of 42 because 42 × 10 = 4200
462462 is a multiple of 42 because 42 × 11 = 4620
504504 is a multiple of 42 because 42 × 12 = 5040
546546 is a multiple of 42 because 42 × 13 = 5460
588588 is a multiple of 42 because 42 × 14 = 5880
630630 is a multiple of 42 because 42 × 15 = 6300
672672 is a multiple of 42 because 42 × 16 = 6720
714714 is a multiple of 42 because 42 × 17 = 7140
756756 is a multiple of 42 because 42 × 18 = 7560
798798 is a multiple of 42 because 42 × 19 = 7980
840840 is a multiple of 42 because 42 × 20 = 8400
882882 is a multiple of 42 because 42 × 21 = 8820
924924 is a multiple of 42 because 42 × 22 = 9240
966966 is a multiple of 42 because 42 × 23 = 9660
10081008 is a multiple of 42 because 42 × 24 = 10080
10501050 is a multiple of 42 because 42 × 25 = 10500
10921092 is a multiple of 42 because 42 × 26 = 10920
11341134 is a multiple of 42 because 42 × 27 = 11340
11761176 is a multiple of 42 because 42 × 28 = 11760
12181218 is a multiple of 42 because 42 × 29 = 12180
12601260 is a multiple of 42 because 42 × 30 = 12600
13021302 is a multiple of 42 because 42 × 31 = 13020
13441344 is a multiple of 42 because 42 × 32 = 13440
13861386 is a multiple of 42 because 42 × 33 = 13860
14281428 is a multiple of 42 because 42 × 34 = 14280
14701470 is a multiple of 42 because 42 × 35 = 14700
15121512 is a multiple of 42 because 42 × 36 = 15120
15541554 is a multiple of 42 because 42 × 37 = 15540
15961596 is a multiple of 42 because 42 × 38 = 15960
16381638 is a multiple of 42 because 42 × 39 = 16380
16801680 is a multiple of 42 because 42 × 40 = 16800
17221722 is a multiple of 42 because 42 × 41 = 17220
17641764 is a multiple of 42 because 42 × 42 = 17640
18061806 is a multiple of 42 because 42 × 43 = 18060
18481848 is a multiple of 42 because 42 × 44 = 18480
18901890 is a multiple of 42 because 42 × 45 = 18900
19321932 is a multiple of 42 because 42 × 46 = 19320
19741974 is a multiple of 42 because 42 × 47 = 19740
20162016 is a multiple of 42 because 42 × 48 = 20160
20582058 is a multiple of 42 because 42 × 49 = 20580
21002100 is a multiple of 42 because 42 × 50 = 21000
21422142 is a multiple of 42 because 42 × 51 = 21420
21842184 is a multiple of 42 because 42 × 52 = 21840
22262226 is a multiple of 42 because 42 × 53 = 22260
22682268 is a multiple of 42 because 42 × 54 = 22680
23102310 is a multiple of 42 because 42 × 55 = 23100
23522352 is a multiple of 42 because 42 × 56 = 23520
23942394 is a multiple of 42 because 42 × 57 = 23940
24362436 is a multiple of 42 because 42 × 58 = 24360
24782478 is a multiple of 42 because 42 × 59 = 24780
25202520 is a multiple of 42 because 42 × 60 = 25200
25622562 is a multiple of 42 because 42 × 61 = 25620
26042604 is a multiple of 42 because 42 × 62 = 26040
26462646 is a multiple of 42 because 42 × 63 = 26460
26882688 is a multiple of 42 because 42 × 64 = 26880
27302730 is a multiple of 42 because 42 × 65 = 27300
27722772 is a multiple of 42 because 42 × 66 = 27720
28142814 is a multiple of 42 because 42 × 67 = 28140
28562856 is a multiple of 42 because 42 × 68 = 28560
28982898 is a multiple of 42 because 42 × 69 = 28980
29402940 is a multiple of 42 because 42 × 70 = 29400
29822982 is a multiple of 42 because 42 × 71 = 29820
30243024 is a multiple of 42 because 42 × 72 = 30240
30663066 is a multiple of 42 because 42 × 73 = 30660
31083108 is a multiple of 42 because 42 × 74 = 31080
31503150 is a multiple of 42 because 42 × 75 = 31500
31923192 is a multiple of 42 because 42 × 76 = 31920
32343234 is a multiple of 42 because 42 × 77 = 32340
32763276 is a multiple of 42 because 42 × 78 = 32760
33183318 is a multiple of 42 because 42 × 79 = 33180
33603360 is a multiple of 42 because 42 × 80 = 33600
34023402 is a multiple of 42 because 42 × 81 = 34020
34443444 is a multiple of 42 because 42 × 82 = 34440
34863486 is a multiple of 42 because 42 × 83 = 34860
35283528 is a multiple of 42 because 42 × 84 = 35280
35703570 is a multiple of 42 because 42 × 85 = 35700
36123612 is a multiple of 42 because 42 × 86 = 36120
36543654 is a multiple of 42 because 42 × 87 = 36540
36963696 is a multiple of 42 because 42 × 88 = 36960
37383738 is a multiple of 42 because 42 × 89 = 37380
37803780 is a multiple of 42 because 42 × 90 = 37800
38223822 is a multiple of 42 because 42 × 91 = 38220
38643864 is a multiple of 42 because 42 × 92 = 38640
39063906 is a multiple of 42 because 42 × 93 = 39060
39483948 is a multiple of 42 because 42 × 94 = 39480
39903990 is a multiple of 42 because 42 × 95 = 39900
40324032 is a multiple of 42 because 42 × 96 = 40320
40744074 is a multiple of 42 because 42 × 97 = 40740
41164116 is a multiple of 42 because 42 × 98 = 41160
41584158 is a multiple of 42 because 42 × 99 = 41580
42004200 is a multiple of 42 because 42 × 100 = 42000

Read More About Multiples of 42

Table 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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