## Multiples of 35

Multiples of 35 are the products obtained when 35 is multiplied by integers. These numbers form a sequence where each term is an integer multiple of 35, showcasing the relationship between multiplication and divisors. Understanding multiples helps in grasping key mathematical concepts such as factors and divisors. These multiples demonstrate how integer operations generate a series of numbers, each divisible by 35 without leaving a remainder.

## What are Multiples of 35?

**Multiples of 35 are the products obtained by multiplying 35 by any integer.** Examples include 35, 70, 105, 140, and so on. These numbers follow the pattern 35n, where n is any integer.

**Prime Factorization of 35:**5 × 7

**First 10 Multiples of 35 are**35, 70, 105, 140, 175, 210, 245, 280, 315, 350.

## For example, 105, 175, 280 and 315 are all multiples of 35, 402 is not a multiple of 35 for the following reasons:

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

105 | 105÷35 = 3 | 105 is a multiple of 35 because it divides evenly. | 0 |

175 | 175÷35 = 5 | 175 is a multiple of 35 because it divides evenly. | 0 |

280 | 280÷35 = 8 | 280 is a multiple of 35 because it divides evenly. | 0 |

315 | 315÷35 = 9 | 315 is a multiple of 35 because it divides evenly. | 0 |

402 | 402÷35 = 11 | 402 is not a multiple of 35 because it does not divide evenly. | 17 |

## List of First 100 Multiples of 35 with Remainders

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

35 | 35 is a multiple of 35 because 35 × 1 = 35 | 0 |

70 | 70 is a multiple of 35 because 35 × 2 = 70 | 0 |

105 | 105 is a multiple of 35 because 35 × 3 = 105 | 0 |

140 | 140 is a multiple of 35 because 35 × 4 = 140 | 0 |

175 | 175 is a multiple of 35 because 35 × 5 = 175 | 0 |

210 | 210 is a multiple of 35 because 35 × 6 = 210 | 0 |

245 | 245 is a multiple of 35 because 35 × 7 = 245 | 0 |

280 | 280 is a multiple of 35 because 35 × 8 = 280 | 0 |

315 | 315 is a multiple of 35 because 35 × 9 = 315 | 0 |

350 | 350 is a multiple of 35 because 35 × 10 = 350 | 0 |

385 | 385 is a multiple of 35 because 35 × 11 = 385 | 0 |

420 | 420 is a multiple of 35 because 35 × 12 = 420 | 0 |

455 | 455 is a multiple of 35 because 35 × 13 = 455 | 0 |

490 | 490 is a multiple of 35 because 35 × 14 = 490 | 0 |

525 | 525 is a multiple of 35 because 35 × 15 = 525 | 0 |

560 | 560 is a multiple of 35 because 35 × 16 = 560 | 0 |

595 | 595 is a multiple of 35 because 35 × 17 = 595 | 0 |

630 | 630 is a multiple of 35 because 35 × 18 = 630 | 0 |

665 | 665 is a multiple of 35 because 35 × 19 = 665 | 0 |

700 | 700 is a multiple of 35 because 35 × 20 = 700 | 0 |

735 | 735 is a multiple of 35 because 35 × 21 = 735 | 0 |

770 | 770 is a multiple of 35 because 35 × 22 = 770 | 0 |

805 | 805 is a multiple of 35 because 35 × 23 = 805 | 0 |

840 | 840 is a multiple of 35 because 35 × 24 = 840 | 0 |

875 | 875 is a multiple of 35 because 35 × 25 = 875 | 0 |

910 | 910 is a multiple of 35 because 35 × 26 = 910 | 0 |

945 | 945 is a multiple of 35 because 35 × 27 = 945 | 0 |

980 | 980 is a multiple of 35 because 35 × 28 = 980 | 0 |

1015 | 1015 is a multiple of 35 because 35 × 29 = 1015 | 0 |

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

1085 | 1085 is a multiple of 35 because 35 × 31 = 1085 | 0 |

1120 | 1120 is a multiple of 35 because 35 × 32 = 1120 | 0 |

1155 | 1155 is a multiple of 35 because 35 × 33 = 1155 | 0 |

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

1225 | 1225 is a multiple of 35 because 35 × 35 = 1225 | 0 |

1260 | 1260 is a multiple of 35 because 35 × 36 = 1260 | 0 |

1295 | 1295 is a multiple of 35 because 35 × 37 = 1295 | 0 |

1330 | 1330 is a multiple of 35 because 35 × 38 = 1330 | 0 |

1365 | 1365 is a multiple of 35 because 35 × 39 = 1365 | 0 |

1400 | 1400 is a multiple of 35 because 35 × 40 = 1400 | 0 |

1435 | 1435 is a multiple of 35 because 35 × 41 = 1435 | 0 |

1470 | 1470 is a multiple of 35 because 35 × 42 = 1470 | 0 |

1505 | 1505 is a multiple of 35 because 35 × 43 = 1505 | 0 |

1540 | 1540 is a multiple of 35 because 35 × 44 = 1540 | 0 |

1575 | 1575 is a multiple of 35 because 35 × 45 = 1575 | 0 |

1610 | 1610 is a multiple of 35 because 35 × 46 = 1610 | 0 |

1645 | 1645 is a multiple of 35 because 35 × 47 = 1645 | 0 |

1680 | 1680 is a multiple of 35 because 35 × 48 = 1680 | 0 |

1715 | 1715 is a multiple of 35 because 35 × 49 = 1715 | 0 |

1750 | 1750 is a multiple of 35 because 35 × 50 = 1750 | 0 |

1785 | 1785 is a multiple of 35 because 35 × 51 = 1785 | 0 |

1820 | 1820 is a multiple of 35 because 35 × 52 = 1820 | 0 |

1855 | 1855 is a multiple of 35 because 35 × 53 = 1855 | 0 |

1890 | 1890 is a multiple of 35 because 35 × 54 = 1890 | 0 |

1925 | 1925 is a multiple of 35 because 35 × 55 = 1925 | 0 |

1960 | 1960 is a multiple of 35 because 35 × 56 = 1960 | 0 |

1995 | 1995 is a multiple of 35 because 35 × 57 = 1995 | 0 |

2030 | 2030 is a multiple of 35 because 35 × 58 = 2030 | 0 |

2065 | 2065 is a multiple of 35 because 35 × 59 = 2065 | 0 |

2100 | 2100 is a multiple of 35 because 35 × 60 = 2100 | 0 |

2135 | 2135 is a multiple of 35 because 35 × 61 = 2135 | 0 |

2170 | 2170 is a multiple of 35 because 35 × 62 = 2170 | 0 |

2205 | 2205 is a multiple of 35 because 35 × 63 = 2205 | 0 |

2240 | 2240 is a multiple of 35 because 35 × 64 = 2240 | 0 |

2275 | 2275 is a multiple of 35 because 35 × 65 = 2275 | 0 |

2310 | 2310 is a multiple of 35 because 35 × 66 = 2310 | 0 |

2345 | 2345 is a multiple of 35 because 35 × 67 = 2345 | 0 |

2380 | 2380 is a multiple of 35 because 35 × 68 = 2380 | 0 |

2415 | 2415 is a multiple of 35 because 35 × 69 = 2415 | 0 |

2450 | 2450 is a multiple of 35 because 35 × 70 = 2450 | 0 |

2485 | 2485 is a multiple of 35 because 35 × 71 = 2485 | 0 |

2520 | 2520 is a multiple of 35 because 35 × 72 = 2520 | 0 |

2555 | 2555 is a multiple of 35 because 35 × 73 = 2555 | 0 |

2590 | 2590 is a multiple of 35 because 35 × 74 = 2590 | 0 |

2625 | 2625 is a multiple of 35 because 35 × 75 = 2625 | 0 |

2660 | 2660 is a multiple of 35 because 35 × 76 = 2660 | 0 |

2695 | 2695 is a multiple of 35 because 35 × 77 = 2695 | 0 |

2730 | 2730 is a multiple of 35 because 35 × 78 = 2730 | 0 |

2765 | 2765 is a multiple of 35 because 35 × 79 = 2765 | 0 |

2800 | 2800 is a multiple of 35 because 35 × 80 = 2800 | 0 |

2835 | 2835 is a multiple of 35 because 35 × 81 = 2835 | 0 |

2870 | 2870 is a multiple of 35 because 35 × 82 = 2870 | 0 |

2905 | 2905 is a multiple of 35 because 35 × 83 = 2905 | 0 |

2940 | 2940 is a multiple of 35 because 35 × 84 = 2940 | 0 |

2975 | 2975 is a multiple of 35 because 35 × 85 = 2975 | 0 |

3010 | 3010 is a multiple of 35 because 35 × 86 = 3010 | 0 |

3045 | 3045 is a multiple of 35 because 35 × 87 = 3045 | 0 |

3080 | 3080 is a multiple of 35 because 35 × 88 = 3080 | 0 |

3115 | 3115 is a multiple of 35 because 35 × 89 = 3115 | 0 |

3150 | 3150 is a multiple of 35 because 35 × 90 = 3150 | 0 |

3185 | 3185 is a multiple of 35 because 35 × 91 = 3185 | 0 |

3220 | 3220 is a multiple of 35 because 35 × 92 = 3220 | 0 |

3255 | 3255 is a multiple of 35 because 35 × 93 = 3255 | 0 |

3290 | 3290 is a multiple of 35 because 35 × 94 = 3290 | 0 |

3325 | 3325 is a multiple of 35 because 35 × 95 = 3325 | 0 |

3360 | 3360 is a multiple of 35 because 35 × 96 = 3360 | 0 |

3395 | 3395 is a multiple of 35 because 35 × 97 = 3395 | 0 |

3430 | 3430 is a multiple of 35 because 35 × 98 = 3430 | 0 |

3465 | 3465 is a multiple of 35 because 35 × 99 = 3465 | 0 |

3500 | 3500 is a multiple of 35 because 35 × 100 = 3500 | 0 |

## Read More About Multiples of 35

## Important Notes

### Understand Multiples:

- Multiples of a number are the products of that number with integers.
- For 35, the multiples are 35×n where n is an integer.

### First Few Multiples:

- Calculate the first few multiples to recognize the pattern: 35×1 = 35, 35×2 = 70, 35×3 = 105, and so on.

### Common Pattern:

- Observe that each multiple of 35 increases by 35: 35,70,105,140,…35, 70, 105, 140.
- General form: 35×n, where n is 1, 2, 3, etc.

### Divisibility Rule:

- A number is a multiple of 35 if it is divisible by both 5 and 7 (since 35 = 5×7).
- Check for divisibility by both 5 and 7 to confirm.

### Applications:

- Multiples of 35 can be useful in problems involving least common multiples, scheduling, and periodic events where intervals are 35 units apart.

## Examples on Multiples of 35

### Simple Multiples

- 35×1 = 35
- 35×2 = 70
- 35×3 = 105

### Larger Multiples

- 35×10 = 350
- 35×20 = 700
- 35×30 = 105

### Real-Life Examples

**Time**: If a task takes 35 minutes to complete and you do it twice, it will take 35×2 = 70 minutes.**Money**: If an item costs 35 dollars and you buy 5 of them, the total cost will be 35×5 = 175 dollars.**Measurements**: If a field is 35 yards long and you have 4 such fields, the total length is 35×4 = 140 yards.

## Practical Examples of Multiples of 35

### What is the 15th multiple of 35?

The 15th multiple of 35 is 35×15 = 525.

### Is 350 a multiple of 35?

Yes, 350 is a multiple of 35 because 35×10 = 350.

### What is the next multiple of 35 after 315?

The next multiple of 35 after 315 is 315+35 = 350.

### Find the 25th multiple of 35.

The 25th multiple of 35 is 35×25 = 875.

### Is 780 a multiple of 35?

No, 780 is not a multiple of 35 because it cannot be expressed as 35×n for any integer n.

## FAQs

## What is a multiple of 35?

A multiple of 35 is any number that can be expressed as 35 times an integer. For example, 35, 70, 105, etc.

## How can I check if a number is a multiple of 35?

A number is a multiple of 35 if it is divisible by both 5 and 7, as 35 = 5×7. The number must pass both the divisibility rules for 5 (ends in 0 or 5) and 7.

## What is the smallest multiple of 35?

The smallest multiple of 35 is 35 itself (35×1 = 35).

## What is the 10th multiple of 35?

The 10th multiple of 35 is 35×10 = 350.

## Is 210 a multiple of 35?

Yes, 210 is a multiple of 35 because 35×6 = 210.

## What is the largest multiple of 35 less than 1000?

The largest multiple of 35 less than 1000 is 35×28 = 980.

## What are the first five multiples of 35?

The first five multiples of 35 are 35, 70, 105, 140, and 175.

## How do multiples of 35 relate to factors?

Multiples of 35 are produced by multiplying 35 by whole numbers (1, 2, 3, …). Factors of 35 are numbers that can be multiplied together to produce 35 (1, 5, 7, 35).

## Can a multiple of 35 be an odd number?

No, multiples of 35 cannot be odd numbers because 35 is an odd number multiplied by another integer, resulting in an odd number.

## What is the sum of the first 5 multiples of 35?

The first five multiples of 35 are 35, 70, 105, 140, and 175. The sum is 35 + 70 + 105 + 140 + 175 = 525.