Multiples of 23

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Created by: Team Maths - Examples.com, Last Updated: July 30, 2024

Multiples of 23

Multiples of 23 are numbers obtained by multiplying 23 by any integer. In mathematics, a multiple is a product of a number and an integer. The sequence of multiples of 23 includes 23, 46, 69, and so on. These numbers are significant in number theory as they illustrate the relationship between multiplication, factors, and divisors. Understanding multiples helps in identifying common factors and solving problems related to divisibility and integer operations.

What are Multiples of 23?

Multiples of 23 are the products obtained when 23 is multiplied by integers (e.g., 23, 46, 69, 92). They form an arithmetic sequence where each term increases by 23. These multiples are essential in understanding factors, divisors, and various mathematical operations involving integers.

Prime factorization of 23: 23 = 1 × 23 First 10 multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230.

For example, 69, 115, 161 and 207 are all multiples of 23, 221 is not a multiple of 23 for the following reasons:

NumberReasonRemainder
6969 is a multiple of 23 because 23×3 = 69.0
115115 is a multiple of 23 because 23×5 = 115.0
161161 is a multiple of 23 because 23×7 = 161.0
207207 is a multiple of 23 because 23×9 = 207.0
221221 is not a multiple of 23 because 221÷23 = 9.14

List of First 100 Multiples of 23 with Remainders

List-of-First-100-Multiples-of-23
NumberReasonRemainder
2323 is a multiple of 23 because 23 × 1 = 230
4646 is a multiple of 23 because 23 × 2 = 460
6969 is a multiple of 23 because 23 × 3 = 690
9292 is a multiple of 23 because 23 × 4 = 920
115115 is a multiple of 23 because 23 × 5 = 1150
138138 is a multiple of 23 because 23 × 6 = 1380
161161 is a multiple of 23 because 23 × 7 = 1610
184184 is a multiple of 23 because 23 × 8 = 1840
207207 is a multiple of 23 because 23 × 9 = 2070
230230 is a multiple of 23 because 23 × 10 = 2300
253253 is a multiple of 23 because 23 × 11 = 2530
276276 is a multiple of 23 because 23 × 12 = 2760
299299 is a multiple of 23 because 23 × 13 = 2990
322322 is a multiple of 23 because 23 × 14 = 3220
345345 is a multiple of 23 because 23 × 15 = 3450
368368 is a multiple of 23 because 23 × 16 = 3680
391391 is a multiple of 23 because 23 × 17 = 3910
414414 is a multiple of 23 because 23 × 18 = 4140
437437 is a multiple of 23 because 23 × 19 = 4370
460460 is a multiple of 23 because 23 × 20 = 4600
483483 is a multiple of 23 because 23 × 21 = 4830
506506 is a multiple of 23 because 23 × 22 = 5060
529529 is a multiple of 23 because 23 × 23 = 5290
552552 is a multiple of 23 because 23 × 24 = 5520
575575 is a multiple of 23 because 23 × 25 = 5750
598598 is a multiple of 23 because 23 × 26 = 5980
621621 is a multiple of 23 because 23 × 27 = 6210
644644 is a multiple of 23 because 23 × 28 = 6440
667667 is a multiple of 23 because 23 × 29 = 6670
690690 is a multiple of 23 because 23 × 30 = 6900
713713 is a multiple of 23 because 23 × 31 = 7130
736736 is a multiple of 23 because 23 × 32 = 7360
759759 is a multiple of 23 because 23 × 33 = 7590
782782 is a multiple of 23 because 23 × 34 = 7820
805805 is a multiple of 23 because 23 × 35 = 8050
828828 is a multiple of 23 because 23 × 36 = 8280
851851 is a multiple of 23 because 23 × 37 = 8510
874874 is a multiple of 23 because 23 × 38 = 8740
897897 is a multiple of 23 because 23 × 39 = 8970
920920 is a multiple of 23 because 23 × 40 = 9200
943943 is a multiple of 23 because 23 × 41 = 9430
966966 is a multiple of 23 because 23 × 42 = 9660
989989 is a multiple of 23 because 23 × 43 = 9890
10121012 is a multiple of 23 because 23 × 44 = 10120
10351035 is a multiple of 23 because 23 × 45 = 10350
10581058 is a multiple of 23 because 23 × 46 = 10580
10811081 is a multiple of 23 because 23 × 47 = 10810
11041104 is a multiple of 23 because 23 × 48 = 11040
11271127 is a multiple of 23 because 23 × 49 = 11270
11501150 is a multiple of 23 because 23 × 50 = 11500
11731173 is a multiple of 23 because 23 × 51 = 11730
11961196 is a multiple of 23 because 23 × 52 = 11960
12191219 is a multiple of 23 because 23 × 53 = 12190
12421242 is a multiple of 23 because 23 × 54 = 12420
12651265 is a multiple of 23 because 23 × 55 = 12650
12881288 is a multiple of 23 because 23 × 56 = 12880
13111311 is a multiple of 23 because 23 × 57 = 13110
13341334 is a multiple of 23 because 23 × 58 = 13340
13571357 is a multiple of 23 because 23 × 59 = 13570
13801380 is a multiple of 23 because 23 × 60 = 13800
14031403 is a multiple of 23 because 23 × 61 = 14030
14261426 is a multiple of 23 because 23 × 62 = 14260
14491449 is a multiple of 23 because 23 × 63 = 14490
14721472 is a multiple of 23 because 23 × 64 = 14720
14951495 is a multiple of 23 because 23 × 65 = 14950
15181518 is a multiple of 23 because 23 × 66 = 15180
15411541 is a multiple of 23 because 23 × 67 = 15410
15641564 is a multiple of 23 because 23 × 68 = 15640
15871587 is a multiple of 23 because 23 × 69 = 15870
16101610 is a multiple of 23 because 23 × 70 = 16100
16331633 is a multiple of 23 because 23 × 71 = 16330
16561656 is a multiple of 23 because 23 × 72 = 16560
16791679 is a multiple of 23 because 23 × 73 = 16790
17021702 is a multiple of 23 because 23 × 74 = 17020
17251725 is a multiple of 23 because 23 × 75 = 17250
17481748 is a multiple of 23 because 23 × 76 = 17480
17711771 is a multiple of 23 because 23 × 77 = 17710
17941794 is a multiple of 23 because 23 × 78 = 17940
18171817 is a multiple of 23 because 23 × 79 = 18170
18401840 is a multiple of 23 because 23 × 80 = 18400
18631863 is a multiple of 23 because 23 × 81 = 18630
18861886 is a multiple of 23 because 23 × 82 = 18860
19091909 is a multiple of 23 because 23 × 83 = 19090
19321932 is a multiple of 23 because 23 × 84 = 19320
19551955 is a multiple of 23 because 23 × 85 = 19550
19781978 is a multiple of 23 because 23 × 86 = 19780
20012001 is a multiple of 23 because 23 × 87 = 20010
20242024 is a multiple of 23 because 23 × 88 = 20240
20472047 is a multiple of 23 because 23 × 89 = 20470
20702070 is a multiple of 23 because 23 × 90 = 20700
20932093 is a multiple of 23 because 23 × 91 = 20930
21162116 is a multiple of 23 because 23 × 92 = 21160
21392139 is a multiple of 23 because 23 × 93 = 21390
21622162 is a multiple of 23 because 23 × 94 = 21620
21852185 is a multiple of 23 because 23 × 95 = 21850
22082208 is a multiple of 23 because 23 × 96 = 22080
22312231 is a multiple of 23 because 23 × 97 = 22310
22542254 is a multiple of 23 because 23 × 98 = 22540
22772277 is a multiple of 23 because 23 × 99 = 22770
23002300 is a multiple of 23 because 23 × 100 = 23000

Read More About Multiples of 23

Table of 23

Important Notes

  • Definition: A multiple of 23 is any number that can be expressed as 23×n, where n is an integer.
  • Sequence: The sequence of multiples of 23 starts at 23 and increases by 23 each time: 23, 46, 69, 92, 115, etc.
  • Divisibility: For a number to be a multiple of 23, it must be divisible by 23 without leaving a remainder.
  • Prime Number: Since 23 is a prime number, its only factors are 1 and 23.
  • Applications: Understanding multiples of 23 is useful in number theory, arithmetic operations, and finding common multiples in problems involving division and multiplication.

Examples on Multiples of 23

Example 1: Calculating the 5th Multiple of 23

  • Step 1: Identify the position of the multiple.
  • Step 2: Multiply 23 by 5.23×5 = 115
  • Result: The 5th multiple of 23 is 115.

Example 2: Checking if 184 is a Multiple of 23

  • Step 1: Divide 184 by 23.184÷23 = 8
  • Step 2: Check if the quotient is an integer without a remainder.
  • Result: Since the quotient is 8 (an integer), 184 is a multiple of 23.

Example 3: Finding the Next Multiple of 23 After 69

  • Step 1: Identify the last known multiple (69).
  • Step 2: Add 23 to the last multiple.69+23 = 92
  • Result: The next multiple of 23 after 69 is 92.

Example 4: Determining if 250 is a Multiple of 23

  • Step 1: Divide 250 by 23.250÷23 = 10.87
  • Step 2: Check the remainder.250÷23 = 10
  • Result: Since the quotient is not an integer and there is a remainder of 20, 250 is not a multiple of 23.

Example 5: Calculating the 12th Multiple of 23

  • Step 1: Identify the position of the multiple.
  • Step 2: Multiply 23 by 12.23×12 = 276
  • Result: The 12th multiple of 23 is 276.

FAQs

What are multiples of 23?

Multiples of 23 are numbers that can be expressed as 23×n, where n is an integer. Examples include 23, 46, 69, 92, and so on.

How do you find multiples of 23?

To find multiples of 23, multiply 23 by any integer. For example, 23×2 = 46 and 23×3 = 69.

Is 46 a multiple of 23?

Yes, 46 is a multiple of 23 because 23×2 = 46.

How can you verify if a number is a multiple of 23?

To verify if a number is a multiple of 23, divide the number by 23. If the quotient is an integer and there is no remainder, it is a multiple of 23.

Are multiples of 23 always even?

No, multiples of 23 are not always even. For example, 23 itself is an odd number.

What is the 10th multiple of 23?

The 10th multiple of 23 is 23×10 = 230.

Is 115 a multiple of 23?

Yes, 115 is a multiple of 23 because 23×5 = 115.

What is the next multiple of 23 after 138?

The next multiple of 23 after 138 is 138+23 = 161.

Why is 69 considered a multiple of 23?

69 is considered a multiple of 23 because 23×3 = 69.

Can a negative number be a multiple of 23?

Yes, negative numbers can be multiples of 23. For example, -23 and -46 are multiples of 23 because 23×−1 = −23 and 23×−2 = −46.

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