Multiples of 35

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

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:

NumberCalculationReasonRemainder
105105÷35 = 3105 is a multiple of 35 because it divides evenly.0
175175÷35 = 5175 is a multiple of 35 because it divides evenly.0
280280÷35 = 8280 is a multiple of 35 because it divides evenly.0
315315÷35 = 9315 is a multiple of 35 because it divides evenly.0
402402÷35 = 11402 is not a multiple of 35 because it does not divide evenly.17

List of First 100 Multiples of 35 with Remainders

List-of-First-100-Multiples-of-35
NumberReasonRemainder
3535 is a multiple of 35 because 35 × 1 = 350
7070 is a multiple of 35 because 35 × 2 = 700
105105 is a multiple of 35 because 35 × 3 = 1050
140140 is a multiple of 35 because 35 × 4 = 1400
175175 is a multiple of 35 because 35 × 5 = 1750
210210 is a multiple of 35 because 35 × 6 = 2100
245245 is a multiple of 35 because 35 × 7 = 2450
280280 is a multiple of 35 because 35 × 8 = 2800
315315 is a multiple of 35 because 35 × 9 = 3150
350350 is a multiple of 35 because 35 × 10 = 3500
385385 is a multiple of 35 because 35 × 11 = 3850
420420 is a multiple of 35 because 35 × 12 = 4200
455455 is a multiple of 35 because 35 × 13 = 4550
490490 is a multiple of 35 because 35 × 14 = 4900
525525 is a multiple of 35 because 35 × 15 = 5250
560560 is a multiple of 35 because 35 × 16 = 5600
595595 is a multiple of 35 because 35 × 17 = 5950
630630 is a multiple of 35 because 35 × 18 = 6300
665665 is a multiple of 35 because 35 × 19 = 6650
700700 is a multiple of 35 because 35 × 20 = 7000
735735 is a multiple of 35 because 35 × 21 = 7350
770770 is a multiple of 35 because 35 × 22 = 7700
805805 is a multiple of 35 because 35 × 23 = 8050
840840 is a multiple of 35 because 35 × 24 = 8400
875875 is a multiple of 35 because 35 × 25 = 8750
910910 is a multiple of 35 because 35 × 26 = 9100
945945 is a multiple of 35 because 35 × 27 = 9450
980980 is a multiple of 35 because 35 × 28 = 9800
10151015 is a multiple of 35 because 35 × 29 = 10150
10501050 is a multiple of 35 because 35 × 30 = 10500
10851085 is a multiple of 35 because 35 × 31 = 10850
11201120 is a multiple of 35 because 35 × 32 = 11200
11551155 is a multiple of 35 because 35 × 33 = 11550
11901190 is a multiple of 35 because 35 × 34 = 11900
12251225 is a multiple of 35 because 35 × 35 = 12250
12601260 is a multiple of 35 because 35 × 36 = 12600
12951295 is a multiple of 35 because 35 × 37 = 12950
13301330 is a multiple of 35 because 35 × 38 = 13300
13651365 is a multiple of 35 because 35 × 39 = 13650
14001400 is a multiple of 35 because 35 × 40 = 14000
14351435 is a multiple of 35 because 35 × 41 = 14350
14701470 is a multiple of 35 because 35 × 42 = 14700
15051505 is a multiple of 35 because 35 × 43 = 15050
15401540 is a multiple of 35 because 35 × 44 = 15400
15751575 is a multiple of 35 because 35 × 45 = 15750
16101610 is a multiple of 35 because 35 × 46 = 16100
16451645 is a multiple of 35 because 35 × 47 = 16450
16801680 is a multiple of 35 because 35 × 48 = 16800
17151715 is a multiple of 35 because 35 × 49 = 17150
17501750 is a multiple of 35 because 35 × 50 = 17500
17851785 is a multiple of 35 because 35 × 51 = 17850
18201820 is a multiple of 35 because 35 × 52 = 18200
18551855 is a multiple of 35 because 35 × 53 = 18550
18901890 is a multiple of 35 because 35 × 54 = 18900
19251925 is a multiple of 35 because 35 × 55 = 19250
19601960 is a multiple of 35 because 35 × 56 = 19600
19951995 is a multiple of 35 because 35 × 57 = 19950
20302030 is a multiple of 35 because 35 × 58 = 20300
20652065 is a multiple of 35 because 35 × 59 = 20650
21002100 is a multiple of 35 because 35 × 60 = 21000
21352135 is a multiple of 35 because 35 × 61 = 21350
21702170 is a multiple of 35 because 35 × 62 = 21700
22052205 is a multiple of 35 because 35 × 63 = 22050
22402240 is a multiple of 35 because 35 × 64 = 22400
22752275 is a multiple of 35 because 35 × 65 = 22750
23102310 is a multiple of 35 because 35 × 66 = 23100
23452345 is a multiple of 35 because 35 × 67 = 23450
23802380 is a multiple of 35 because 35 × 68 = 23800
24152415 is a multiple of 35 because 35 × 69 = 24150
24502450 is a multiple of 35 because 35 × 70 = 24500
24852485 is a multiple of 35 because 35 × 71 = 24850
25202520 is a multiple of 35 because 35 × 72 = 25200
25552555 is a multiple of 35 because 35 × 73 = 25550
25902590 is a multiple of 35 because 35 × 74 = 25900
26252625 is a multiple of 35 because 35 × 75 = 26250
26602660 is a multiple of 35 because 35 × 76 = 26600
26952695 is a multiple of 35 because 35 × 77 = 26950
27302730 is a multiple of 35 because 35 × 78 = 27300
27652765 is a multiple of 35 because 35 × 79 = 27650
28002800 is a multiple of 35 because 35 × 80 = 28000
28352835 is a multiple of 35 because 35 × 81 = 28350
28702870 is a multiple of 35 because 35 × 82 = 28700
29052905 is a multiple of 35 because 35 × 83 = 29050
29402940 is a multiple of 35 because 35 × 84 = 29400
29752975 is a multiple of 35 because 35 × 85 = 29750
30103010 is a multiple of 35 because 35 × 86 = 30100
30453045 is a multiple of 35 because 35 × 87 = 30450
30803080 is a multiple of 35 because 35 × 88 = 30800
31153115 is a multiple of 35 because 35 × 89 = 31150
31503150 is a multiple of 35 because 35 × 90 = 31500
31853185 is a multiple of 35 because 35 × 91 = 31850
32203220 is a multiple of 35 because 35 × 92 = 32200
32553255 is a multiple of 35 because 35 × 93 = 32550
32903290 is a multiple of 35 because 35 × 94 = 32900
33253325 is a multiple of 35 because 35 × 95 = 33250
33603360 is a multiple of 35 because 35 × 96 = 33600
33953395 is a multiple of 35 because 35 × 97 = 33950
34303430 is a multiple of 35 because 35 × 98 = 34300
34653465 is a multiple of 35 because 35 × 99 = 34650
35003500 is a multiple of 35 because 35 × 100 = 35000

Read More About Multiples of 35

Table 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.

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