Multiples of 30

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

Multiples of 30

In mathematics, multiples of 30 are the products obtained by multiplying 30 by integers. These numbers play a crucial role in understanding various concepts such as multiplication, divisors, and factors. A multiple of 30 is any number that can be expressed as 30n, where ‘n’ is an integer. Multiples of 30 include numbers like 30, 60, 90, and so on, each sharing common factors with 30. Understanding multiples helps in solving problems related to number theory and arithmetic operations.

What are Multiples of 30?

Multiples of 30 are the products obtained by multiplying 30 by any integer. Examples include 30, 60, 90, 120, and so on. These numbers follow the pattern 30n, where n is any integer.

Prime Factorization of 30: 2 × 3 × 5 First 10 Multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300.

For example, 90, 150, 180 and 270 are all multiples of 30, 473 is not a multiple of 30 for the following reasons:

NumberCalculationReasonRemainder
9090÷30 = 390 is a multiple of 30 because it divides evenly.0
150150÷30 = 5150 is a multiple of 30 because it divides evenly.0
180180÷30 = 6180 is a multiple of 30 because it divides evenly.0
270270÷30 = 9270 is a multiple of 30 because it divides evenly.0
473473÷30 = 15473 is not a multiple of 30 because it does not divide evenly.23

List of First 100 Multiples of 30 with Remainders

List-of-First-100-Multiples-of-30
NumberReasonRemainder
3030 is a multiple of 30 because 30 × 1 = 300
6060 is a multiple of 30 because 30 × 2 = 600
9090 is a multiple of 30 because 30 × 3 = 900
120120 is a multiple of 30 because 30 × 4 = 1200
150150 is a multiple of 30 because 30 × 5 = 1500
180180 is a multiple of 30 because 30 × 6 = 1800
210210 is a multiple of 30 because 30 × 7 = 2100
240240 is a multiple of 30 because 30 × 8 = 2400
270270 is a multiple of 30 because 30 × 9 = 2700
300300 is a multiple of 30 because 30 × 10 = 3000
330330 is a multiple of 30 because 30 × 11 = 3300
360360 is a multiple of 30 because 30 × 12 = 3600
390390 is a multiple of 30 because 30 × 13 = 3900
420420 is a multiple of 30 because 30 × 14 = 4200
450450 is a multiple of 30 because 30 × 15 = 4500
480480 is a multiple of 30 because 30 × 16 = 4800
510510 is a multiple of 30 because 30 × 17 = 5100
540540 is a multiple of 30 because 30 × 18 = 5400
570570 is a multiple of 30 because 30 × 19 = 5700
600600 is a multiple of 30 because 30 × 20 = 6000
630630 is a multiple of 30 because 30 × 21 = 6300
660660 is a multiple of 30 because 30 × 22 = 6600
690690 is a multiple of 30 because 30 × 23 = 6900
720720 is a multiple of 30 because 30 × 24 = 7200
750750 is a multiple of 30 because 30 × 25 = 7500
780780 is a multiple of 30 because 30 × 26 = 7800
810810 is a multiple of 30 because 30 × 27 = 8100
840840 is a multiple of 30 because 30 × 28 = 8400
870870 is a multiple of 30 because 30 × 29 = 8700
900900 is a multiple of 30 because 30 × 30 = 9000
930930 is a multiple of 30 because 30 × 31 = 9300
960960 is a multiple of 30 because 30 × 32 = 9600
990990 is a multiple of 30 because 30 × 33 = 9900
10201020 is a multiple of 30 because 30 × 34 = 10200
10501050 is a multiple of 30 because 30 × 35 = 10500
10801080 is a multiple of 30 because 30 × 36 = 10800
11101110 is a multiple of 30 because 30 × 37 = 11100
11401140 is a multiple of 30 because 30 × 38 = 11400
11701170 is a multiple of 30 because 30 × 39 = 11700
12001200 is a multiple of 30 because 30 × 40 = 12000
12301230 is a multiple of 30 because 30 × 41 = 12300
12601260 is a multiple of 30 because 30 × 42 = 12600
12901290 is a multiple of 30 because 30 × 43 = 12900
13201320 is a multiple of 30 because 30 × 44 = 13200
13501350 is a multiple of 30 because 30 × 45 = 13500
13801380 is a multiple of 30 because 30 × 46 = 13800
14101410 is a multiple of 30 because 30 × 47 = 14100
14401440 is a multiple of 30 because 30 × 48 = 14400
14701470 is a multiple of 30 because 30 × 49 = 14700
15001500 is a multiple of 30 because 30 × 50 = 15000
15301530 is a multiple of 30 because 30 × 51 = 15300
15601560 is a multiple of 30 because 30 × 52 = 15600
15901590 is a multiple of 30 because 30 × 53 = 15900
16201620 is a multiple of 30 because 30 × 54 = 16200
16501650 is a multiple of 30 because 30 × 55 = 16500
16801680 is a multiple of 30 because 30 × 56 = 16800
17101710 is a multiple of 30 because 30 × 57 = 17100
17401740 is a multiple of 30 because 30 × 58 = 17400
17701770 is a multiple of 30 because 30 × 59 = 17700
18001800 is a multiple of 30 because 30 × 60 = 18000
18301830 is a multiple of 30 because 30 × 61 = 18300
18601860 is a multiple of 30 because 30 × 62 = 18600
18901890 is a multiple of 30 because 30 × 63 = 18900
19201920 is a multiple of 30 because 30 × 64 = 19200
19501950 is a multiple of 30 because 30 × 65 = 19500
19801980 is a multiple of 30 because 30 × 66 = 19800
20102010 is a multiple of 30 because 30 × 67 = 20100
20402040 is a multiple of 30 because 30 × 68 = 20400
20702070 is a multiple of 30 because 30 × 69 = 20700
21002100 is a multiple of 30 because 30 × 70 = 21000
21302130 is a multiple of 30 because 30 × 71 = 21300
21602160 is a multiple of 30 because 30 × 72 = 21600
21902190 is a multiple of 30 because 30 × 73 = 21900
22202220 is a multiple of 30 because 30 × 74 = 22200
22502250 is a multiple of 30 because 30 × 75 = 22500
22802280 is a multiple of 30 because 30 × 76 = 22800
23102310 is a multiple of 30 because 30 × 77 = 23100
23402340 is a multiple of 30 because 30 × 78 = 23400
23702370 is a multiple of 30 because 30 × 79 = 23700
24002400 is a multiple of 30 because 30 × 80 = 24000
24302430 is a multiple of 30 because 30 × 81 = 24300
24602460 is a multiple of 30 because 30 × 82 = 24600
24902490 is a multiple of 30 because 30 × 83 = 24900
25202520 is a multiple of 30 because 30 × 84 = 25200
25502550 is a multiple of 30 because 30 × 85 = 25500
25802580 is a multiple of 30 because 30 × 86 = 25800
26102610 is a multiple of 30 because 30 × 87 = 26100
26402640 is a multiple of 30 because 30 × 88 = 26400
26702670 is a multiple of 30 because 30 × 89 = 26700
27002700 is a multiple of 30 because 30 × 90 = 27000
27302730 is a multiple of 30 because 30 × 91 = 27300
27602760 is a multiple of 30 because 30 × 92 = 27600
27902790 is a multiple of 30 because 30 × 93 = 27900
28202820 is a multiple of 30 because 30 × 94 = 28200
28502850 is a multiple of 30 because 30 × 95 = 28500
28802880 is a multiple of 30 because 30 × 96 = 28800
29102910 is a multiple of 30 because 30 × 97 = 29100
29402940 is a multiple of 30 because 30 × 98 = 29400
29702970 is a multiple of 30 because 30 × 99 = 29700
30003000 is a multiple of 30 because 30 × 100 = 30000

Read More About Multiples of 30

Table of 30

Important Notes

Definition: A multiple of 30 is any number that can be expressed as 30×n, where n is an integer. This means that the multiples of 30 include numbers like 30, 60, 90, 120, and so on.

Common Factors: Multiples of 30 have common factors of 1, 2, 3, 5, 6, 10, 15, and 30. This is because 30 is the product of its prime factors 2×3×5.

Divisibility: A number is a multiple of 30 if it is divisible by both 3 and 10. To check for divisibility by 3, the sum of the digits should be divisible by 3. To check for divisibility by 10, the number must end in 0.

Pattern: The multiples of 30 follow a simple pattern where each multiple increases by 30. For example, starting from 30, the sequence is 30, 60, 90, 120, 150, etc.

Applications: Multiples of 30 are used in various practical applications such as time (minutes in an hour), measurements, and in contexts where grouping or scheduling occurs in intervals of 30 units.

Examples on Multiples of 30

Simple Multiples

  • 1 × 30 = 30
  • 2 × 30 = 60
  • 3 × 30 = 90

Larger Multiples

  • 10 × 30 = 300
  • 20 × 30 = 600

Real-Life Examples

  • Time: 60 minutes in an hour is a multiple of 30 because 2 × 30 = 60.
  • Money: $30 is a multiple of 30 because 1 × 30 = 30.
  • Weight: 300 grams is a multiple of 30 because 10 × 30 = 300.

Practical Examples of Multiples of 30

What is the 5th multiple of 30?

The 5th multiple of 30 is 5 × 30 = 150.

Is 90 a multiple of 30?

Yes, 90 is a multiple of 30 because 3 × 30 = 90.

What is the next multiple of 30 after 150?

The next multiple of 30 after 150 is 150 + 30 = 180.

Find the 8th multiple of 30.

The 8th multiple of 30 is 8 × 30 = 240.

Is 85 a multiple of 30?

No, 85 is not a multiple of 30 because it cannot be expressed as 30 × n where n is an integer.

FAQs

What is a multiple of 30?

A multiple of 30 is any number that can be expressed as 30 times an integer, such as 30, 60, 90, etc.

A multiple of 30 is any number that can be expressed as 30 times an integer, such as 30, 60, 90, etc.

A number is a multiple of 30 if it is divisible by both 2, 3, and 5, since 30 = 2 × 3 × 5.

What is the smallest positive multiple of 30?

The smallest positive multiple of 30 is 30 itself (30 × 1 = 30).

What is the 10th multiple of 30?

The 10th multiple of 30 is 30 × 10 = 300.

Is 150 a multiple of 30?

Yes, 150 is a multiple of 30 because 30 × 5 = 150.

What is the next multiple of 30 after 300?

The next multiple of 30 after 300 is 300 + 30 = 330.

Are all multiples of 30 also multiples of 10?

Yes, all multiples of 30 are also multiples of 10 because 30 is a multiple of 10.

What is the least common multiple (LCM) of 30 and 45?

The least common multiple (LCM) of 30 and 45 is 90.

Is 200 a multiple of 30?

No, 200 is not a multiple of 30 because it cannot be expressed as 30 × n for any integer n.

How do you find the common multiples of 30 and another number, such as 50?

To find the common multiples of 30 and 50, you can calculate their least common multiple (LCM). For 30 and 50, the LCM is 150. Therefore, common multiples are 150, 300, 450, etc.

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