Multiples of 26

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

Multiples of 26

Multiples of 26 are integers that result from multiplying 26 by other whole numbers. In mathematics, these multiples play a crucial role in understanding number patterns and relationships. Each multiple of 26 is both a product of 26 and an integer divisor of larger numbers. Factors of 26 itself are 1, 2, 13, and 26, and its multiples are obtained through their multiplication with other integers. Recognizing these multiples helps in solving various mathematical problems related to division, factors, and common multiples.

What are Multiples of 26?

Multiples of 26 are numbers obtained by multiplying 26 by any integer. These include 26, 52, 78, 104, 130, and so on. In general, a multiple of 26 is in the form 26n, where n is an integer.

Prime factorization of 26: 26 = 2 × 13 First 10 multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260.

For example, 78, 130, 156 and 234 are all multiples of 26, 265 is not a multiple of 26 for the following reasons:

Here’s the table format with the remainder last:

NumberCalculationReasonRemainder
7878÷26 = 378 is a multiple of 26 because it divides evenly.0
130130÷26 = 5130 is a multiple of 26 because it divides evenly.0
156156÷26 = 6156 is a multiple of 26 because it divides evenly.0
234234÷26 = 9234 is a multiple of 26 because it divides evenly.0
265265÷26 = 10265 is not a multiple of 26 because it does not divide evenly.5

List of First 100 Multiples of 26 with Remainders

List-of-First-100-Multiples-of-26
NumberReasonRemainder
2626 is a multiple of 26 because 26 × 1 = 260
5252 is a multiple of 26 because 26 × 2 = 520
7878 is a multiple of 26 because 26 × 3 = 780
104104 is a multiple of 26 because 26 × 4 = 1040
130130 is a multiple of 26 because 26 × 5 = 1300
156156 is a multiple of 26 because 26 × 6 = 1560
182182 is a multiple of 26 because 26 × 7 = 1820
208208 is a multiple of 26 because 26 × 8 = 2080
234234 is a multiple of 26 because 26 × 9 = 2340
260260 is a multiple of 26 because 26 × 10 = 2600
286286 is a multiple of 26 because 26 × 11 = 2860
312312 is a multiple of 26 because 26 × 12 = 3120
338338 is a multiple of 26 because 26 × 13 = 3380
364364 is a multiple of 26 because 26 × 14 = 3640
390390 is a multiple of 26 because 26 × 15 = 3900
416416 is a multiple of 26 because 26 × 16 = 4160
442442 is a multiple of 26 because 26 × 17 = 4420
468468 is a multiple of 26 because 26 × 18 = 4680
494494 is a multiple of 26 because 26 × 19 = 4940
520520 is a multiple of 26 because 26 × 20 = 5200
546546 is a multiple of 26 because 26 × 21 = 5460
572572 is a multiple of 26 because 26 × 22 = 5720
598598 is a multiple of 26 because 26 × 23 = 5980
624624 is a multiple of 26 because 26 × 24 = 6240
650650 is a multiple of 26 because 26 × 25 = 6500
676676 is a multiple of 26 because 26 × 26 = 6760
702702 is a multiple of 26 because 26 × 27 = 7020
728728 is a multiple of 26 because 26 × 28 = 7280
754754 is a multiple of 26 because 26 × 29 = 7540
780780 is a multiple of 26 because 26 × 30 = 7800
806806 is a multiple of 26 because 26 × 31 = 8060
832832 is a multiple of 26 because 26 × 32 = 8320
858858 is a multiple of 26 because 26 × 33 = 8580
884884 is a multiple of 26 because 26 × 34 = 8840
910910 is a multiple of 26 because 26 × 35 = 9100
936936 is a multiple of 26 because 26 × 36 = 9360
962962 is a multiple of 26 because 26 × 37 = 9620
988988 is a multiple of 26 because 26 × 38 = 9880
10141014 is a multiple of 26 because 26 × 39 = 10140
10401040 is a multiple of 26 because 26 × 40 = 10400
10661066 is a multiple of 26 because 26 × 41 = 10660
10921092 is a multiple of 26 because 26 × 42 = 10920
11181118 is a multiple of 26 because 26 × 43 = 11180
11441144 is a multiple of 26 because 26 × 44 = 11440
11701170 is a multiple of 26 because 26 × 45 = 11700
11961196 is a multiple of 26 because 26 × 46 = 11960
12221222 is a multiple of 26 because 26 × 47 = 12220
12481248 is a multiple of 26 because 26 × 48 = 12480
12741274 is a multiple of 26 because 26 × 49 = 12740
13001300 is a multiple of 26 because 26 × 50 = 13000
13261326 is a multiple of 26 because 26 × 51 = 13260
13521352 is a multiple of 26 because 26 × 52 = 13520
13781378 is a multiple of 26 because 26 × 53 = 13780
14041404 is a multiple of 26 because 26 × 54 = 14040
14301430 is a multiple of 26 because 26 × 55 = 14300
14561456 is a multiple of 26 because 26 × 56 = 14560
14821482 is a multiple of 26 because 26 × 57 = 14820
15081508 is a multiple of 26 because 26 × 58 = 15080
15341534 is a multiple of 26 because 26 × 59 = 15340
15601560 is a multiple of 26 because 26 × 60 = 15600
15861586 is a multiple of 26 because 26 × 61 = 15860
16121612 is a multiple of 26 because 26 × 62 = 16120
16381638 is a multiple of 26 because 26 × 63 = 16380
16641664 is a multiple of 26 because 26 × 64 = 16640
16901690 is a multiple of 26 because 26 × 65 = 16900
17161716 is a multiple of 26 because 26 × 66 = 17160
17421742 is a multiple of 26 because 26 × 67 = 17420
17681768 is a multiple of 26 because 26 × 68 = 17680
17941794 is a multiple of 26 because 26 × 69 = 17940
18201820 is a multiple of 26 because 26 × 70 = 18200
18461846 is a multiple of 26 because 26 × 71 = 18460
18721872 is a multiple of 26 because 26 × 72 = 18720
18981898 is a multiple of 26 because 26 × 73 = 18980
19241924 is a multiple of 26 because 26 × 74 = 19240
19501950 is a multiple of 26 because 26 × 75 = 19500
19761976 is a multiple of 26 because 26 × 76 = 19760
20022002 is a multiple of 26 because 26 × 77 = 20020
20282028 is a multiple of 26 because 26 × 78 = 20280
20542054 is a multiple of 26 because 26 × 79 = 20540
20802080 is a multiple of 26 because 26 × 80 = 20800
21062106 is a multiple of 26 because 26 × 81 = 21060
21322132 is a multiple of 26 because 26 × 82 = 21320
21582158 is a multiple of 26 because 26 × 83 = 21580
21842184 is a multiple of 26 because 26 × 84 = 21840
22102210 is a multiple of 26 because 26 × 85 = 22100
22362236 is a multiple of 26 because 26 × 86 = 22360
22622262 is a multiple of 26 because 26 × 87 = 22620
22882288 is a multiple of 26 because 26 × 88 = 22880
23142314 is a multiple of 26 because 26 × 89 = 23140
23402340 is a multiple of 26 because 26 × 90 = 23400
23662366 is a multiple of 26 because 26 × 91 = 23660
23922392 is a multiple of 26 because 26 × 92 = 23920
24182418 is a multiple of 26 because 26 × 93 = 24180
24442444 is a multiple of 26 because 26 × 94 = 24440
24702470 is a multiple of 26 because 26 × 95 = 24700
24962496 is a multiple of 26 because 26 × 96 = 24960
25222522 is a multiple of 26 because 26 × 97 = 25220
25482548 is a multiple of 26 because 26 × 98 = 25480
25742574 is a multiple of 26 because 26 × 99 = 25740
26002600 is a multiple of 26 because 26 × 100 = 26000

Read More About Multiples of 26

Table of 26

Important Notes

1. Definition of Multiples

  • Multiples of a number are the results you get when you multiply that number by an integer.
  • Example: The multiples of 26 are 26, 52, 78, 104, etc.

2. Generating Multiples

  • To generate the multiples of 26, simply multiply 26 by positive integers.
  • Formula: 26×n26 \times n26×n where nnn is an integer (1, 2, 3,…).

3. Sequence Pattern

  • The sequence of multiples of 26 forms an arithmetic sequence where each term increases by 26.
  • Example: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260.

4. Properties of Multiples

  • Divisibility: Any multiple of 26 is also divisible by 2 and 13 since 26 = 2×13.
  • Even Numbers: All multiples of 26 are even because 26 itself is an even number.

5. Applications in Real Life

  • Grouping and Batching: Multiples of 26 can be useful in situations where items are grouped in sets of 26.
  • Common Multiples: Useful for finding common time intervals or measurements in various fields such as science, engineering, and economics.

Examples on Multiples of 26

Example 1: Finding Specific Multiples

Problem: Identify the 15th multiple of 26.
To find the 15th multiple of 26, multiply 26 by 15. 26×15 = 390

The 15th multiple of 26 is 390.

Example 2: Common Multiples

Problem: Find the smallest common multiple of 26 and 13.
Since 13 is a factor of 26, the smallest common multiple is the larger number, which is 26.
The smallest common multiple of 26 and 13 is 26.

Example 3: Divisibility Check

Problem: Determine if 104 is a multiple of 26.
To check if 104 is a multiple of 26, divide 104 by 26. 104÷26 = 4 Since the result is a whole number with no remainder, 104 is a multiple of 26.

Yes, 104 is a multiple of 26.

Example 4: Application in Real-Life Situations

Problem: A factory packs 26 bottles in each box. How many bottles are there in 50 boxes?
To find the total number of bottles, multiply the number of boxes by the number of bottles per box. 26×50 = 1300.

There are 1300 bottles in 50 boxes.

Example 5: Sequences

Problem: List the first 5 multiples of 26.
Calculate the first 5 multiples by multiplying 26 by 1, 2, 3, 4, and 5:

  • 26×1 = 26
  • 26×2 = 52
  • 26×3 = 78
  • 26×4 = 104
  • 26×5 = 130

The first 5 multiples of 26 are 26, 52, 78, 104, and 130.

Example 6: Finding Multiples within a Range

Problem: Identify all multiples of 26 between 100 and 300.
Start with the smallest multiple of 26 greater than or equal to 100, which is 104. Continue adding 26 until reaching the largest multiple less than or equal to 300:

  • 26×4 = 104
  • 26×5 = 130
  • 26×6 = 156
  • 26×7 = 182
  • 26×8 = 208
  • 26×9 = 234
  • 26×10 = 260
  • 26×11 = 286.

The multiples of 26 between 100 and 300 are 104, 130, 156, 182, 208, 234, 260, and 286.

FAQs

What is a multiple of 26?

A multiple of 26 is a number that can be expressed as 26 times an integer. Examples include 26, 52, 78, and 104.

How do you find multiples of 26?

To find multiples of 26, multiply 26 by any integer (positive, negative, or zero). For example, 26 × 3 = 78 and 26 × (-2) = -52.

Is 104 a multiple of 26?

Yes, 104 is a multiple of 26 because 104 ÷ 26 equals 4, which is an integer.

Are all multiples of 26 even numbers?

Yes, all multiples of 26 are even numbers because 26 itself is an even number, and the product of an even number with any integer is always even.

What is the smallest positive multiple of 26?

The smallest positive multiple of 26 is 26 itself (26 × 1).

Are multiples of 26 also multiples of 2 and 13?

Yes, since 26 is the product of 2 and 13 (26 = 2 × 13), any multiple of 26 is also a multiple of both 2 and 13.

Can a multiple of 26 be a decimal?

No, multiples of 26 are always integers. Multiplying 26 by any integer will always result in an integer.

What is the 10th multiple of 26?

The 10th multiple of 26 is 260 (26 × 10).

Is 0 a multiple of 26?

Yes, 0 is a multiple of every integer, including 26, because 26 × 0 = 0.

How many multiples of 26 are there between 100 and 300?

There are 8 multiples of 26 between 100 and 300: 104, 130, 156, 182, 208, 234, 260, and 286.

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