## 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:

Number | Calculation | Reason | Remainder |
---|---|---|---|

90 | 90÷30 = 3 | 90 is a multiple of 30 because it divides evenly. | 0 |

150 | 150÷30 = 5 | 150 is a multiple of 30 because it divides evenly. | 0 |

180 | 180÷30 = 6 | 180 is a multiple of 30 because it divides evenly. | 0 |

270 | 270÷30 = 9 | 270 is a multiple of 30 because it divides evenly. | 0 |

473 | 473÷30 = 15 | 473 is not a multiple of 30 because it does not divide evenly. | 23 |

## List of First 100 Multiples of 30 with Remainders

Number | Reason | Remainder |
---|---|---|

30 | 30 is a multiple of 30 because 30 × 1 = 30 | 0 |

60 | 60 is a multiple of 30 because 30 × 2 = 60 | 0 |

90 | 90 is a multiple of 30 because 30 × 3 = 90 | 0 |

120 | 120 is a multiple of 30 because 30 × 4 = 120 | 0 |

150 | 150 is a multiple of 30 because 30 × 5 = 150 | 0 |

180 | 180 is a multiple of 30 because 30 × 6 = 180 | 0 |

210 | 210 is a multiple of 30 because 30 × 7 = 210 | 0 |

240 | 240 is a multiple of 30 because 30 × 8 = 240 | 0 |

270 | 270 is a multiple of 30 because 30 × 9 = 270 | 0 |

300 | 300 is a multiple of 30 because 30 × 10 = 300 | 0 |

330 | 330 is a multiple of 30 because 30 × 11 = 330 | 0 |

360 | 360 is a multiple of 30 because 30 × 12 = 360 | 0 |

390 | 390 is a multiple of 30 because 30 × 13 = 390 | 0 |

420 | 420 is a multiple of 30 because 30 × 14 = 420 | 0 |

450 | 450 is a multiple of 30 because 30 × 15 = 450 | 0 |

480 | 480 is a multiple of 30 because 30 × 16 = 480 | 0 |

510 | 510 is a multiple of 30 because 30 × 17 = 510 | 0 |

540 | 540 is a multiple of 30 because 30 × 18 = 540 | 0 |

570 | 570 is a multiple of 30 because 30 × 19 = 570 | 0 |

600 | 600 is a multiple of 30 because 30 × 20 = 600 | 0 |

630 | 630 is a multiple of 30 because 30 × 21 = 630 | 0 |

660 | 660 is a multiple of 30 because 30 × 22 = 660 | 0 |

690 | 690 is a multiple of 30 because 30 × 23 = 690 | 0 |

720 | 720 is a multiple of 30 because 30 × 24 = 720 | 0 |

750 | 750 is a multiple of 30 because 30 × 25 = 750 | 0 |

780 | 780 is a multiple of 30 because 30 × 26 = 780 | 0 |

810 | 810 is a multiple of 30 because 30 × 27 = 810 | 0 |

840 | 840 is a multiple of 30 because 30 × 28 = 840 | 0 |

870 | 870 is a multiple of 30 because 30 × 29 = 870 | 0 |

900 | 900 is a multiple of 30 because 30 × 30 = 900 | 0 |

930 | 930 is a multiple of 30 because 30 × 31 = 930 | 0 |

960 | 960 is a multiple of 30 because 30 × 32 = 960 | 0 |

990 | 990 is a multiple of 30 because 30 × 33 = 990 | 0 |

1020 | 1020 is a multiple of 30 because 30 × 34 = 1020 | 0 |

1050 | 1050 is a multiple of 30 because 30 × 35 = 1050 | 0 |

1080 | 1080 is a multiple of 30 because 30 × 36 = 1080 | 0 |

1110 | 1110 is a multiple of 30 because 30 × 37 = 1110 | 0 |

1140 | 1140 is a multiple of 30 because 30 × 38 = 1140 | 0 |

1170 | 1170 is a multiple of 30 because 30 × 39 = 1170 | 0 |

1200 | 1200 is a multiple of 30 because 30 × 40 = 1200 | 0 |

1230 | 1230 is a multiple of 30 because 30 × 41 = 1230 | 0 |

1260 | 1260 is a multiple of 30 because 30 × 42 = 1260 | 0 |

1290 | 1290 is a multiple of 30 because 30 × 43 = 1290 | 0 |

1320 | 1320 is a multiple of 30 because 30 × 44 = 1320 | 0 |

1350 | 1350 is a multiple of 30 because 30 × 45 = 1350 | 0 |

1380 | 1380 is a multiple of 30 because 30 × 46 = 1380 | 0 |

1410 | 1410 is a multiple of 30 because 30 × 47 = 1410 | 0 |

1440 | 1440 is a multiple of 30 because 30 × 48 = 1440 | 0 |

1470 | 1470 is a multiple of 30 because 30 × 49 = 1470 | 0 |

1500 | 1500 is a multiple of 30 because 30 × 50 = 1500 | 0 |

1530 | 1530 is a multiple of 30 because 30 × 51 = 1530 | 0 |

1560 | 1560 is a multiple of 30 because 30 × 52 = 1560 | 0 |

1590 | 1590 is a multiple of 30 because 30 × 53 = 1590 | 0 |

1620 | 1620 is a multiple of 30 because 30 × 54 = 1620 | 0 |

1650 | 1650 is a multiple of 30 because 30 × 55 = 1650 | 0 |

1680 | 1680 is a multiple of 30 because 30 × 56 = 1680 | 0 |

1710 | 1710 is a multiple of 30 because 30 × 57 = 1710 | 0 |

1740 | 1740 is a multiple of 30 because 30 × 58 = 1740 | 0 |

1770 | 1770 is a multiple of 30 because 30 × 59 = 1770 | 0 |

1800 | 1800 is a multiple of 30 because 30 × 60 = 1800 | 0 |

1830 | 1830 is a multiple of 30 because 30 × 61 = 1830 | 0 |

1860 | 1860 is a multiple of 30 because 30 × 62 = 1860 | 0 |

1890 | 1890 is a multiple of 30 because 30 × 63 = 1890 | 0 |

1920 | 1920 is a multiple of 30 because 30 × 64 = 1920 | 0 |

1950 | 1950 is a multiple of 30 because 30 × 65 = 1950 | 0 |

1980 | 1980 is a multiple of 30 because 30 × 66 = 1980 | 0 |

2010 | 2010 is a multiple of 30 because 30 × 67 = 2010 | 0 |

2040 | 2040 is a multiple of 30 because 30 × 68 = 2040 | 0 |

2070 | 2070 is a multiple of 30 because 30 × 69 = 2070 | 0 |

2100 | 2100 is a multiple of 30 because 30 × 70 = 2100 | 0 |

2130 | 2130 is a multiple of 30 because 30 × 71 = 2130 | 0 |

2160 | 2160 is a multiple of 30 because 30 × 72 = 2160 | 0 |

2190 | 2190 is a multiple of 30 because 30 × 73 = 2190 | 0 |

2220 | 2220 is a multiple of 30 because 30 × 74 = 2220 | 0 |

2250 | 2250 is a multiple of 30 because 30 × 75 = 2250 | 0 |

2280 | 2280 is a multiple of 30 because 30 × 76 = 2280 | 0 |

2310 | 2310 is a multiple of 30 because 30 × 77 = 2310 | 0 |

2340 | 2340 is a multiple of 30 because 30 × 78 = 2340 | 0 |

2370 | 2370 is a multiple of 30 because 30 × 79 = 2370 | 0 |

2400 | 2400 is a multiple of 30 because 30 × 80 = 2400 | 0 |

2430 | 2430 is a multiple of 30 because 30 × 81 = 2430 | 0 |

2460 | 2460 is a multiple of 30 because 30 × 82 = 2460 | 0 |

2490 | 2490 is a multiple of 30 because 30 × 83 = 2490 | 0 |

2520 | 2520 is a multiple of 30 because 30 × 84 = 2520 | 0 |

2550 | 2550 is a multiple of 30 because 30 × 85 = 2550 | 0 |

2580 | 2580 is a multiple of 30 because 30 × 86 = 2580 | 0 |

2610 | 2610 is a multiple of 30 because 30 × 87 = 2610 | 0 |

2640 | 2640 is a multiple of 30 because 30 × 88 = 2640 | 0 |

2670 | 2670 is a multiple of 30 because 30 × 89 = 2670 | 0 |

2700 | 2700 is a multiple of 30 because 30 × 90 = 2700 | 0 |

2730 | 2730 is a multiple of 30 because 30 × 91 = 2730 | 0 |

2760 | 2760 is a multiple of 30 because 30 × 92 = 2760 | 0 |

2790 | 2790 is a multiple of 30 because 30 × 93 = 2790 | 0 |

2820 | 2820 is a multiple of 30 because 30 × 94 = 2820 | 0 |

2850 | 2850 is a multiple of 30 because 30 × 95 = 2850 | 0 |

2880 | 2880 is a multiple of 30 because 30 × 96 = 2880 | 0 |

2910 | 2910 is a multiple of 30 because 30 × 97 = 2910 | 0 |

2940 | 2940 is a multiple of 30 because 30 × 98 = 2940 | 0 |

2970 | 2970 is a multiple of 30 because 30 × 99 = 2970 | 0 |

3000 | 3000 is a multiple of 30 because 30 × 100 = 3000 | 0 |

## Read More About Multiples 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.