Multiples of 105

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Created by: Team Maths - Examples.com, Last Updated: August 22, 2024

Multiples of 105

Multiples of 105 are numbers that can be obtained by multiplying 105 with any integer. These multiples include 105, 210, 315, and so on, forming an infinite sequence. Understanding multiples involves the concepts of multiplication, where 105 acts as a base number. The factors and divisors of 105, such as 1, 3, 5, 7, 15, 21, 35, and 105 itself, play a crucial role in determining its multiples. Learning about multiples is essential in various mathematical applications, including finding common denominators and solving problems related to divisibility.

What are Multiples of 105?

Multiples of 105 are the products obtained when 105 is multiplied by whole numbers, such as 1, 2, 3, and so on. In mathematics, these multiples are numbers like 105, 210, 315, and continue infinitely. They are integral in understanding the concepts of multiplication, factors, and divisors.

Prime Factorization of 105: 3 × 5 × 7 First 10 Multiples of 105 are 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050.

For example, 420, 630, 735 and 945 are all multiples of 105, 1032 is not a multiple of 105 for the following reasons:

NumberCalculationReasonRemainder
420420÷105 = 4420 is a multiple of 105 because it divides evenly.0
630630÷105 = 6630 is a multiple of 105 because it divides evenly.0
735735÷105 = 7735 is a multiple of 105 because it divides evenly.0
945945÷105 = 9945 is a multiple of 105 because it divides evenly.0
10321032÷105 = 91032 is not a multiple of 105 because it does not divide evenly.87

List of First 100 Multiples of 105 with Remainders

List-of-First-100-Multiples-of-105
NumberReasonRemainder
105105 is a multiple of 105 because 105 × 1 = 1050
210210 is a multiple of 105 because 105 × 2 = 2100
315315 is a multiple of 105 because 105 × 3 = 3150
420420 is a multiple of 105 because 105 × 4 = 4200
525525 is a multiple of 105 because 105 × 5 = 5250
630630 is a multiple of 105 because 105 × 6 = 6300
735735 is a multiple of 105 because 105 × 7 = 7350
840840 is a multiple of 105 because 105 × 8 = 8400
945945 is a multiple of 105 because 105 × 9 = 9450
10501050 is a multiple of 105 because 105 × 10 = 10500
11551155 is a multiple of 105 because 105 × 11 = 11550
12601260 is a multiple of 105 because 105 × 12 = 12600
13651365 is a multiple of 105 because 105 × 13 = 13650
14701470 is a multiple of 105 because 105 × 14 = 14700
15751575 is a multiple of 105 because 105 × 15 = 15750
16801680 is a multiple of 105 because 105 × 16 = 16800
17851785 is a multiple of 105 because 105 × 17 = 17850
18901890 is a multiple of 105 because 105 × 18 = 18900
19951995 is a multiple of 105 because 105 × 19 = 19950
21002100 is a multiple of 105 because 105 × 20 = 21000
22052205 is a multiple of 105 because 105 × 21 = 22050
23102310 is a multiple of 105 because 105 × 22 = 23100
24152415 is a multiple of 105 because 105 × 23 = 24150
25202520 is a multiple of 105 because 105 × 24 = 25200
26252625 is a multiple of 105 because 105 × 25 = 26250
27302730 is a multiple of 105 because 105 × 26 = 27300
28352835 is a multiple of 105 because 105 × 27 = 28350
29402940 is a multiple of 105 because 105 × 28 = 29400
30453045 is a multiple of 105 because 105 × 29 = 30450
31503150 is a multiple of 105 because 105 × 30 = 31500
32553255 is a multiple of 105 because 105 × 31 = 32550
33603360 is a multiple of 105 because 105 × 32 = 33600
34653465 is a multiple of 105 because 105 × 33 = 34650
35703570 is a multiple of 105 because 105 × 34 = 35700
36753675 is a multiple of 105 because 105 × 35 = 36750
37803780 is a multiple of 105 because 105 × 36 = 37800
38853885 is a multiple of 105 because 105 × 37 = 38850
39903990 is a multiple of 105 because 105 × 38 = 39900
40954095 is a multiple of 105 because 105 × 39 = 40950
42004200 is a multiple of 105 because 105 × 40 = 42000
43054305 is a multiple of 105 because 105 × 41 = 43050
44104410 is a multiple of 105 because 105 × 42 = 44100
45154515 is a multiple of 105 because 105 × 43 = 45150
46204620 is a multiple of 105 because 105 × 44 = 46200
47254725 is a multiple of 105 because 105 × 45 = 47250
48304830 is a multiple of 105 because 105 × 46 = 48300
49354935 is a multiple of 105 because 105 × 47 = 49350
50405040 is a multiple of 105 because 105 × 48 = 50400
51455145 is a multiple of 105 because 105 × 49 = 51450
52505250 is a multiple of 105 because 105 × 50 = 52500
53555355 is a multiple of 105 because 105 × 51 = 53550
54605460 is a multiple of 105 because 105 × 52 = 54600
55655565 is a multiple of 105 because 105 × 53 = 55650
56705670 is a multiple of 105 because 105 × 54 = 56700
57755775 is a multiple of 105 because 105 × 55 = 57750
58805880 is a multiple of 105 because 105 × 56 = 58800
59855985 is a multiple of 105 because 105 × 57 = 59850
60906090 is a multiple of 105 because 105 × 58 = 60900
61956195 is a multiple of 105 because 105 × 59 = 61950
63006300 is a multiple of 105 because 105 × 60 = 63000
64056405 is a multiple of 105 because 105 × 61 = 64050
65106510 is a multiple of 105 because 105 × 62 = 65100
66156615 is a multiple of 105 because 105 × 63 = 66150
67206720 is a multiple of 105 because 105 × 64 = 67200
68256825 is a multiple of 105 because 105 × 65 = 68250
69306930 is a multiple of 105 because 105 × 66 = 69300
70357035 is a multiple of 105 because 105 × 67 = 70350
71407140 is a multiple of 105 because 105 × 68 = 71400
72457245 is a multiple of 105 because 105 × 69 = 72450
73507350 is a multiple of 105 because 105 × 70 = 73500
74557455 is a multiple of 105 because 105 × 71 = 74550
75607560 is a multiple of 105 because 105 × 72 = 75600
76657665 is a multiple of 105 because 105 × 73 = 76650
77707770 is a multiple of 105 because 105 × 74 = 77700
78757875 is a multiple of 105 because 105 × 75 = 78750
79807980 is a multiple of 105 because 105 × 76 = 79800
80858085 is a multiple of 105 because 105 × 77 = 80850
81908190 is a multiple of 105 because 105 × 78 = 81900
82958295 is a multiple of 105 because 105 × 79 = 82950
84008400 is a multiple of 105 because 105 × 80 = 84000
85058505 is a multiple of 105 because 105 × 81 = 85050
86108610 is a multiple of 105 because 105 × 82 = 86100
87158715 is a multiple of 105 because 105 × 83 = 87150
88208820 is a multiple of 105 because 105 × 84 = 88200
89258925 is a multiple of 105 because 105 × 85 = 89250
90309030 is a multiple of 105 because 105 × 86 = 90300
91359135 is a multiple of 105 because 105 × 87 = 91350
92409240 is a multiple of 105 because 105 × 88 = 92400
93459345 is a multiple of 105 because 105 × 89 = 93450
94509450 is a multiple of 105 because 105 × 90 = 94500
95559555 is a multiple of 105 because 105 × 91 = 95550
96609660 is a multiple of 105 because 105 × 92 = 96600
97659765 is a multiple of 105 because 105 × 93 = 97650
98709870 is a multiple of 105 because 105 × 94 = 98700
99759975 is a multiple of 105 because 105 × 95 = 99750
1008010080 is a multiple of 105 because 105 × 96 = 100800
1018510185 is a multiple of 105 because 105 × 97 = 101850
1029010290 is a multiple of 105 because 105 × 98 = 102900
1039510395 is a multiple of 105 because 105 × 99 = 103950
1050010500 is a multiple of 105 because 105 × 100 = 105000

Read More About Multiples of 105

Table of 105

Important Notes

Definition of Multiples

  • A multiple of a number is the product of that number and an integer.
  • For example, the multiples of 105 are obtained by multiplying 105 by integers: 105×1 = 105, 105×2 = 210, 105×3 = 315, and so on.

Properties of Multiples of 105

  • Divisibility: Every multiple of 105 is divisible by 105, 5, 7, and 3 (since 105=3×5×7105 = 3 \times 5 \times 7105=3×5×7).
  • Common Multiples: Multiples of 105 can also be considered common multiples of 3, 5, and 7.

First Few Multiples of 105

The first few multiples of 105 are:

  • 105 (105 × 1)
  • 210 (105 × 2)
  • 315 (105 × 3)
  • 420 (105 × 4)
  • 525 (105 × 5)

Recognizing Multiples of 105

A number is a multiple of 105 if:

  • It ends in 0 or 5 (divisible by 5).
  • The sum of its digits is divisible by 3.
  • The number is divisible by 7.

For example, 210:

  • Ends in 0 (divisible by 5).
  • Sum of digits: 2 + 1 + 0 = 3 (divisible by 3).
  • Divisible by 7 (210 ÷ 7 = 30).

Applications of Multiples of 105

  • LCM and GCD: Multiples of 105 are useful when finding the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) involving the numbers 3, 5, and 7.
  • Pattern Recognition: Recognizing patterns in multiples of 105 can simplify complex arithmetic and algebraic problems.

Examples on Multiples of 105

First Ten Multiples of 105:

  • 105 × 1 = 105
  • 105 × 2 = 210
  • 105 × 3 = 315
  • 105 × 4 = 420
  • 105 × 5 = 525
  • 105 × 6 = 630
  • 105 × 7 = 735
  • 105 × 8 = 840
  • 105 × 9 = 945
  • 105 × 10 = 1050

Properties and Patterns:

Additive Property: The sum of two multiples of 105 is also a multiple of 105.

  • Example: 210 + 420 = 630 (both 210 and 420 are multiples of 105, and so is 630).

Subtracting Property: The difference between two multiples of 105 is also a multiple of 105.

  • Example: 840 – 525 = 315 (both 840 and 525 are multiples of 105, and so is 315).

Real-world Applications:

Scheduling: If an event occurs every 105 days, the schedule can be determined using multiples of 105.

  • Example: If an event starts on January 1st, the next occurrence will be on April 16th (105 days later), then on July 30th (210 days later), and so on.

Bulk Quantities: In manufacturing, ordering parts in multiples of 105 can help in inventory management.

  • Example: If a factory orders screws in batches of 105, ordering 5 batches means they receive 525 screws (5 × 105).

Large Multiples:

  • 105 × 20 = 2100
  • 105 × 50 = 5250
  • 105 × 100 = 10500
  • 105 × 500 = 52500

Practical Example in Measurements:

Distance: If a car travels 105 miles in one trip, then over multiple trips, the distance covered can be calculated using multiples of 105.

  • Example: Over 3 trips, the car travels 315 miles (105 × 3 = 315).

Summary Table of First 20 Multiples of 105

MultiplierMultiple of 105
1105
2210
3315
4420
5525
6630
7735
8840
9945
101050
111155
121260
131365
141470
151575
161680
171785
181890
191995
202100

FAQs

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