## Multiples of 34

In mathematics, multiples of 34 are numbers that can be obtained by multiplying 34 with any integer. These numbers are the result of the multiplication of 34 with whole numbers such as 1, 2, 3, and so on. Each multiple of 34 can also be described as having 34 as one of its factors or divisors. Understanding multiples is fundamental to grasping more complex concepts in number theory and arithmetic.

## What are Multiples of 34?

**Multiples of 34 are the products obtained by multiplying 34 by any integer.** Examples include 34, 68, 102, 136, and so on. These numbers follow the pattern 34n, where n is any integer.

**Prime Factorization of 34:**2 x 17

**First 10 Multiples of 34 are**34, 68, 102, 136, 170, 204, 238, 272, 306, 340.

## For example, 102, 170, 238 and 272 are all multiples of 34, 360 is not a multiple of 34 for the following reasons:

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

102 | 102÷34 = 3 | 102 is a multiple of 34 because it divides evenly. | 0 |

170 | 170÷34 = 5 | 170 is a multiple of 34 because it divides evenly. | 0 |

238 | 238÷34 = 7 | 238 is a multiple of 34 because it divides evenly. | 0 |

272 | 272÷34 = 8 | 272 is a multiple of 34 because it divides evenly. | 0 |

360 | 360÷34 = 10 | 360 is not a multiple of 34 because it does not divide evenly. | 20 |

## List of First 100 Multiples of 34 with Remainders

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

34 | 34 is a multiple of 34 because 34 × 1 = 34 | 0 |

68 | 68 is a multiple of 34 because 34 × 2 = 68 | 0 |

102 | 102 is a multiple of 34 because 34 × 3 = 102 | 0 |

136 | 136 is a multiple of 34 because 34 × 4 = 136 | 0 |

170 | 170 is a multiple of 34 because 34 × 5 = 170 | 0 |

204 | 204 is a multiple of 34 because 34 × 6 = 204 | 0 |

238 | 238 is a multiple of 34 because 34 × 7 = 238 | 0 |

272 | 272 is a multiple of 34 because 34 × 8 = 272 | 0 |

306 | 306 is a multiple of 34 because 34 × 9 = 306 | 0 |

340 | 340 is a multiple of 34 because 34 × 10 = 340 | 0 |

374 | 374 is a multiple of 34 because 34 × 11 = 374 | 0 |

408 | 408 is a multiple of 34 because 34 × 12 = 408 | 0 |

442 | 442 is a multiple of 34 because 34 × 13 = 442 | 0 |

476 | 476 is a multiple of 34 because 34 × 14 = 476 | 0 |

510 | 510 is a multiple of 34 because 34 × 15 = 510 | 0 |

544 | 544 is a multiple of 34 because 34 × 16 = 544 | 0 |

578 | 578 is a multiple of 34 because 34 × 17 = 578 | 0 |

612 | 612 is a multiple of 34 because 34 × 18 = 612 | 0 |

646 | 646 is a multiple of 34 because 34 × 19 = 646 | 0 |

680 | 680 is a multiple of 34 because 34 × 20 = 680 | 0 |

714 | 714 is a multiple of 34 because 34 × 21 = 714 | 0 |

748 | 748 is a multiple of 34 because 34 × 22 = 748 | 0 |

782 | 782 is a multiple of 34 because 34 × 23 = 782 | 0 |

816 | 816 is a multiple of 34 because 34 × 24 = 816 | 0 |

850 | 850 is a multiple of 34 because 34 × 25 = 850 | 0 |

884 | 884 is a multiple of 34 because 34 × 26 = 884 | 0 |

918 | 918 is a multiple of 34 because 34 × 27 = 918 | 0 |

952 | 952 is a multiple of 34 because 34 × 28 = 952 | 0 |

986 | 986 is a multiple of 34 because 34 × 29 = 986 | 0 |

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

1054 | 1054 is a multiple of 34 because 34 × 31 = 1054 | 0 |

1088 | 1088 is a multiple of 34 because 34 × 32 = 1088 | 0 |

1122 | 1122 is a multiple of 34 because 34 × 33 = 1122 | 0 |

1156 | 1156 is a multiple of 34 because 34 × 34 = 1156 | 0 |

1190 | 1190 is a multiple of 34 because 34 × 35 = 1190 | 0 |

1224 | 1224 is a multiple of 34 because 34 × 36 = 1224 | 0 |

1258 | 1258 is a multiple of 34 because 34 × 37 = 1258 | 0 |

1292 | 1292 is a multiple of 34 because 34 × 38 = 1292 | 0 |

1326 | 1326 is a multiple of 34 because 34 × 39 = 1326 | 0 |

1360 | 1360 is a multiple of 34 because 34 × 40 = 1360 | 0 |

1394 | 1394 is a multiple of 34 because 34 × 41 = 1394 | 0 |

1428 | 1428 is a multiple of 34 because 34 × 42 = 1428 | 0 |

1462 | 1462 is a multiple of 34 because 34 × 43 = 1462 | 0 |

1496 | 1496 is a multiple of 34 because 34 × 44 = 1496 | 0 |

1530 | 1530 is a multiple of 34 because 34 × 45 = 1530 | 0 |

1564 | 1564 is a multiple of 34 because 34 × 46 = 1564 | 0 |

1598 | 1598 is a multiple of 34 because 34 × 47 = 1598 | 0 |

1632 | 1632 is a multiple of 34 because 34 × 48 = 1632 | 0 |

1666 | 1666 is a multiple of 34 because 34 × 49 = 1666 | 0 |

1700 | 1700 is a multiple of 34 because 34 × 50 = 1700 | 0 |

1734 | 1734 is a multiple of 34 because 34 × 51 = 1734 | 0 |

1768 | 1768 is a multiple of 34 because 34 × 52 = 1768 | 0 |

1802 | 1802 is a multiple of 34 because 34 × 53 = 1802 | 0 |

1836 | 1836 is a multiple of 34 because 34 × 54 = 1836 | 0 |

1870 | 1870 is a multiple of 34 because 34 × 55 = 1870 | 0 |

1904 | 1904 is a multiple of 34 because 34 × 56 = 1904 | 0 |

1938 | 1938 is a multiple of 34 because 34 × 57 = 1938 | 0 |

1972 | 1972 is a multiple of 34 because 34 × 58 = 1972 | 0 |

2006 | 2006 is a multiple of 34 because 34 × 59 = 2006 | 0 |

2040 | 2040 is a multiple of 34 because 34 × 60 = 2040 | 0 |

2074 | 2074 is a multiple of 34 because 34 × 61 = 2074 | 0 |

2108 | 2108 is a multiple of 34 because 34 × 62 = 2108 | 0 |

2142 | 2142 is a multiple of 34 because 34 × 63 = 2142 | 0 |

2176 | 2176 is a multiple of 34 because 34 × 64 = 2176 | 0 |

2210 | 2210 is a multiple of 34 because 34 × 65 = 2210 | 0 |

2244 | 2244 is a multiple of 34 because 34 × 66 = 2244 | 0 |

2278 | 2278 is a multiple of 34 because 34 × 67 = 2278 | 0 |

2312 | 2312 is a multiple of 34 because 34 × 68 = 2312 | 0 |

2346 | 2346 is a multiple of 34 because 34 × 69 = 2346 | 0 |

2380 | 2380 is a multiple of 34 because 34 × 70 = 2380 | 0 |

2414 | 2414 is a multiple of 34 because 34 × 71 = 2414 | 0 |

2448 | 2448 is a multiple of 34 because 34 × 72 = 2448 | 0 |

2482 | 2482 is a multiple of 34 because 34 × 73 = 2482 | 0 |

2516 | 2516 is a multiple of 34 because 34 × 74 = 2516 | 0 |

2550 | 2550 is a multiple of 34 because 34 × 75 = 2550 | 0 |

2584 | 2584 is a multiple of 34 because 34 × 76 = 2584 | 0 |

2618 | 2618 is a multiple of 34 because 34 × 77 = 2618 | 0 |

2652 | 2652 is a multiple of 34 because 34 × 78 = 2652 | 0 |

2686 | 2686 is a multiple of 34 because 34 × 79 = 2686 | 0 |

2720 | 2720 is a multiple of 34 because 34 × 80 = 2720 | 0 |

2754 | 2754 is a multiple of 34 because 34 × 81 = 2754 | 0 |

2788 | 2788 is a multiple of 34 because 34 × 82 = 2788 | 0 |

2822 | 2822 is a multiple of 34 because 34 × 83 = 2822 | 0 |

2856 | 2856 is a multiple of 34 because 34 × 84 = 2856 | 0 |

2890 | 2890 is a multiple of 34 because 34 × 85 = 2890 | 0 |

2924 | 2924 is a multiple of 34 because 34 × 86 = 2924 | 0 |

2958 | 2958 is a multiple of 34 because 34 × 87 = 2958 | 0 |

2992 | 2992 is a multiple of 34 because 34 × 88 = 2992 | 0 |

3026 | 3026 is a multiple of 34 because 34 × 89 = 3026 | 0 |

3060 | 3060 is a multiple of 34 because 34 × 90 = 3060 | 0 |

3094 | 3094 is a multiple of 34 because 34 × 91 = 3094 | 0 |

3128 | 3128 is a multiple of 34 because 34 × 92 = 3128 | 0 |

3162 | 3162 is a multiple of 34 because 34 × 93 = 3162 | 0 |

3196 | 3196 is a multiple of 34 because 34 × 94 = 3196 | 0 |

3230 | 3230 is a multiple of 34 because 34 × 95 = 3230 | 0 |

3264 | 3264 is a multiple of 34 because 34 × 96 = 3264 | 0 |

3298 | 3298 is a multiple of 34 because 34 × 97 = 3298 | 0 |

3332 | 3332 is a multiple of 34 because 34 × 98 = 3332 | 0 |

3366 | 3366 is a multiple of 34 because 34 × 99 = 3366 | 0 |

3400 | 3400 is a multiple of 34 because 34 × 100 = 3400 | 0 |

## Read More About Multiples of 34

## Important Notes

**Definition**: Multiples of 34 are the products of 34 and any integer. For example, 34, 68, 102, 136, etc.

**Pattern**: The sequence of multiples of 34 increases by 34 each time. If n is an integer, then the n-th multiple of 34 is 34×n.

**Common Properties**:

- All multiples of 34 are even numbers because 34 itself is even.
- If a number is a multiple of 34, it is also a multiple of 2 and 17, since 34 = 2 × 17.

**Divisibility**:

- A number is a multiple of 34 if it can be evenly divided by 34 without a remainder.
- To check if a large number is a multiple of 34, you can divide the number by 34 and see if the quotient is an integer.

**Applications**: Multiples of 34 can be used in various mathematical problems, including finding common multiples, solving least common multiple (LCM) problems, and understanding number patterns and sequences.

## Examples on Multiples of 34

### Simple Multiples

- 34 × 2 = 68
- 34 × 3 = 102
- 34 × 4 = 136

### Larger Multiples

- 34 × 5 = 170

34 × 6 = 204

### Real-Life Examples

**Age**: If you have a family with 34 members, then the total age of 6 members is a multiple of 34, e.g., 34 × 6 = 204.**Money**: Suppose you have a currency denomination where each bill is 34 units. If you have 10 such bills, the total is 34 × 10 = 340.**Time**: In an event that lasts 34 minutes, if repeated 5 times, the total time spent is a multiple of 34, e.g., 34 × 5 = 170.

## Practical Examples of Multiples of 34

### What is the 10th multiple of 34?

The 10th multiple of 34 is 34 × 10 = 340.

### Is 238 a multiple of 34?

Yes, 238 is a multiple of 34 because 34 × 7 = 238.

### What is the next multiple of 34 after 204?

The next multiple of 34 after 204 is 204 + 34 = 238.

### Find the 15th multiple of 34.

The 15th multiple of 34 is 34 × 15 = 510.

### Is 73 a multiple of 34?

No, 73 is not a multiple of 34 because it cannot be expressed as 34 × n, where n is an integer.

## FAQs

## What is a multiple of 34?

A multiple of 34 is any number that can be expressed as 34 times an integer, such as 34, 68, 102, etc.

## How can you determine if a number is a multiple of 34?

To determine if a number is a multiple of 34, divide the number by 34. If the result is an integer, the number is a multiple of 34.

## What are the first five multiples of 34?

The first five multiples of 34 are 34, 68, 102, 136, and 170.

## The first five multiples of 34 are 34, 68, 102, 136, and 170.

Yes, 204 is a multiple of 34 because 34×6 = 204.

## What is the 10th multiple of 34?

The 10th multiple of 34 is 34×10 = 340.

## Are all multiples of 34 even numbers?

Yes, since 34 is an even number, all of its multiples are also even numbers.

## What is the least common multiple (LCM) of 34 and 51?

The least common multiple of 34 and 51 is 34×51 / GCD(34, 51) = 34×51 / 17 = 102.

## How do you find the common multiples of 34 and another number?

To find the common multiples of 34 and another number, calculate the least common multiple (LCM) of the two numbers.

## Can a multiple of 34 be a prime number?

No, a multiple of 34 cannot be a prime number because it is divisible by 34 and thus has at least three divisors: 1, 34, and itself.

## What is the next multiple of 34 after 340?

The next multiple of 34 after 340 is 340+34 = 374.