What is the smallest multiple of 67 that is greater than 100?
134
201
268
335
of 10
Multiples of 67
Multiples of 67
Multiples of 67 are numbers that can be expressed as 67×𝑛 where 𝑛n is an integer. These multiples increase by 67 each time (e.g., 67, 134, 201, 268, 335) and are not necessarily even. In mathematics, particularly in algebra, squares, square roots, and fractions, multiples of 67 are crucial. They help in understanding numbers properties and performing various arithmetic operations efficiently. Recognizing these multiples aids in grasping complex mathematical ideas and solving algebraic equations. Multiples of 67 serve as essential building blocks in number theory, helping to explore patterns, relationships, and the behavior of numbers within mathematical frameworks. This understanding is fundamental to advancing in mathematics and developing problem-solving skills.
What are Multiples of 67?
Multiples of 67 are numbers that can be expressed as 67×n, where n is an integer. These numbers are always even and include values like 67, 134, 201, 268, and so on.
Prime Factorization of 67 : 1 & 67
First 10 Multiples of 67 are 67, 134, 201, 268, 335, 402, 469, 536, 603, 670.
First 50 Multiples of 67 are 67, 134, 201, 268, 335, 402, 469, 536, 603, 670, 737, 804, 871, 938, 1005, 1072, 1139, 1206, 1273, 1340, 1407, 1474, 1541, 1608, 1675, 1742, 1809, 1876, 1943, 2010, 2077, 2144, 2211, 2278, 2345, 2412, 2479, 2546, 2613, 2680, 2747, 2814, 2881, 2948, 3015, 3082, 3149, 3216, 3283, 3350
For example, 67, 134, 201 and 268 are all multiples of 67, 134 is not a multiple of 66 for the following reasons:
| Number | Reason | Remainder |
|---|---|---|
| 67 | 67 × 1 = 67, so it is a multiple of 67. | 0 |
| 134 | 67 × 2 = 134, so it is a multiple of 67. | 0 |
| 201 | 67 × 3 = 201, so it is a multiple of 67. | 0 |
| 268 | 67 × 4 = 268, so it is a multiple of 67. | 0 |
| 134 | 134 ÷ 66 = 2.0303, not an integer. | 2 |
List of First 100 Multiples of 67 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 67 | 67 × 1 = 67, so it is a multiple of 67. | 0 |
| 134 | 67 × 2 = 134, so it is a multiple of 67. | 0 |
| 201 | 67 × 3 = 201, so it is a multiple of 67. | 0 |
| 268 | 67 × 4 = 268, so it is a multiple of 67. | 0 |
| 335 | 67 × 5 = 335, so it is a multiple of 67. | 0 |
| 402 | 67 × 6 = 402, so it is a multiple of 67. | 0 |
| 469 | 67 × 7 = 469, so it is a multiple of 67. | 0 |
| 536 | 67 × 8 = 536, so it is a multiple of 67. | 0 |
| 603 | 67 × 9 = 603, so it is a multiple of 67. | 0 |
| 670 | 67 × 10 = 670, so it is a multiple of 67. | 0 |
| 737 | 67 × 11 = 737, so it is a multiple of 67. | 0 |
| 804 | 67 × 12 = 804, so it is a multiple of 67. | 0 |
| 871 | 67 × 13 = 871, so it is a multiple of 67. | 0 |
| 938 | 67 × 14 = 938, so it is a multiple of 67. | 0 |
| 1005 | 67 × 15 = 1005, so it is a multiple of 67. | 0 |
| 1072 | 67 × 16 = 1072, so it is a multiple of 67. | 0 |
| 1139 | 67 × 17 = 1139, so it is a multiple of 67. | 0 |
| 1206 | 67 × 18 = 1206, so it is a multiple of 67. | 0 |
| 1273 | 67 × 19 = 1273, so it is a multiple of 67. | 0 |
| 1340 | 67 × 20 = 1340, so it is a multiple of 67. | 0 |
| 1407 | 67 × 21 = 1407, so it is a multiple of 67. | 0 |
| 1474 | 67 × 22 = 1474, so it is a multiple of 67. | 0 |
| 1541 | 67 × 23 = 1541, so it is a multiple of 67. | 0 |
| 1608 | 67 × 24 = 1608, so it is a multiple of 67. | 0 |
| 1675 | 67 × 25 = 1675, so it is a multiple of 67. | 0 |
| 1742 | 67 × 26 = 1742, so it is a multiple of 67. | 0 |
| 1809 | 67 × 27 = 1809, so it is a multiple of 67. | 0 |
| 1876 | 67 × 28 = 1876, so it is a multiple of 67. | 0 |
| 1943 | 67 × 29 = 1943, so it is a multiple of 67. | 0 |
| 2010 | 67 × 30 = 2010, so it is a multiple of 67. | 0 |
| 2077 | 67 × 31 = 2077, so it is a multiple of 67. | 0 |
| 2144 | 67 × 32 = 2144, so it is a multiple of 67. | 0 |
| 2211 | 67 × 33 = 2211, so it is a multiple of 67. | 0 |
| 2278 | 67 × 34 = 2278, so it is a multiple of 67. | 0 |
| 2345 | 67 × 35 = 2345, so it is a multiple of 67. | 0 |
| 2412 | 67 × 36 = 2412, so it is a multiple of 67. | 0 |
| 2479 | 67 × 37 = 2479, so it is a multiple of 67. | 0 |
| 2546 | 67 × 38 = 2546, so it is a multiple of 67. | 0 |
| 2613 | 67 × 39 = 2613, so it is a multiple of 67. | 0 |
| 2680 | 67 × 40 = 2680, so it is a multiple of 67. | 0 |
| 2747 | 67 × 41 = 2747, so it is a multiple of 67. | 0 |
| 2814 | 67 × 42 = 2814, so it is a multiple of 67. | 0 |
| 2881 | 67 × 43 = 2881, so it is a multiple of 67. | 0 |
| 2948 | 67 × 44 = 2948, so it is a multiple of 67. | 0 |
| 3015 | 67 × 45 = 3015, so it is a multiple of 67. | 0 |
| 3082 | 67 × 46 = 3082, so it is a multiple of 67. | 0 |
| 3149 | 67 × 47 = 3149, so it is a multiple of 67. | 0 |
| 3216 | 67 × 48 = 3216, so it is a multiple of 67. | 0 |
| 3283 | 67 × 49 = 3283, so it is a multiple of 67. | 0 |
| 3350 | 67 × 50 = 3350, so it is a multiple of 67. | 0 |
| 3417 | 67 × 51 = 3417, so it is a multiple of 67. | 0 |
| 3484 | 67 × 52 = 3484, so it is a multiple of 67. | 0 |
| 3551 | 67 × 53 = 3551, so it is a multiple of 67. | 0 |
| 3618 | 67 × 54 = 3618, so it is a multiple of 67. | 0 |
| 3685 | 67 × 55 = 3685, so it is a multiple of 67. | 0 |
| 3752 | 67 × 56 = 3752, so it is a multiple of 67. | 0 |
| 3819 | 67 × 57 = 3819, so it is a multiple of 67. | 0 |
| 3886 | 67 × 58 = 3886, so it is a multiple of 67. | 0 |
| 3953 | 67 × 59 = 3953, so it is a multiple of 67. | 0 |
| 4020 | 67 × 60 = 4020, so it is a multiple of 67. | 0 |
| 4087 | 67 × 61 = 4087, so it is a multiple of 67. | 0 |
| 4154 | 67 × 62 = 4154, so it is a multiple of 67. | 0 |
| 4221 | 67 × 63 = 4221, so it is a multiple of 67. | 0 |
| 4288 | 67 × 64 = 4288, so it is a multiple of 67. | 0 |
| 4355 | 67 × 65 = 4355, so it is a multiple of 67. | 0 |
| 4422 | 67 × 66 = 4422, so it is a multiple of 67. | 0 |
| 4489 | 67 × 67 = 4489, so it is a multiple of 67. | 0 |
| 4556 | 67 × 68 = 4556, so it is a multiple of 67. | 0 |
| 4623 | 67 × 69 = 4623, so it is a multiple of 67. | 0 |
| 4690 | 67 × 70 = 4690, so it is a multiple of 67. | 0 |
| 4757 | 67 × 71 = 4757, so it is a multiple of 67. | 0 |
| 4824 | 67 × 72 = 4824, so it is a multiple of 67. | 0 |
| 4891 | 67 × 73 = 4891, so it is a multiple of 67. | 0 |
| 4958 | 67 × 74 = 4958, so it is a multiple of 67. | 0 |
| 5025 | 67 × 75 = 5025, so it is a multiple of 67. | 0 |
| 5092 | 67 × 76 = 5092, so it is a multiple of 67. | 0 |
| 5159 | 67 × 77 = 5159, so it is a multiple of 67. | 0 |
| 5226 | 67 × 78 = 5226, so it is a multiple of 67. | 0 |
| 5293 | 67 × 79 = 5293, so it is a multiple of 67. | 0 |
| 5360 | 67 × 80 = 5360, so it is a multiple of 67. | 0 |
| 5427 | 67 × 81 = 5427, so it is a multiple of 67. | 0 |
| 5494 | 67 × 82 = 5494, so it is a multiple of 67. | 0 |
| 5561 | 67 × 83 = 5561, so it is a multiple of 67. | 0 |
| 5628 | 67 × 84 = 5628, so it is a multiple of 67. | 0 |
| 5695 | 67 × 85 = 5695, so it is a multiple of 67. | 0 |
| 5762 | 67 × 86 = 5762, so it is a multiple of 67. | 0 |
| 5829 | 67 × 87 = 5829, so it is a multiple of 67. | 0 |
| 5896 | 67 × 88 = 5896, so it is a multiple of 67. | 0 |
| 5963 | 67 × 89 = 5963, so it is a multiple of 67. | 0 |
| 6030 | 67 × 90 = 6030, so it is a multiple of 67. | 0 |
| 6097 | 67 × 91 = 6097, so it is a multiple of 67. | 0 |
| 6164 | 67 × 92 = 6164, so it is a multiple of 67. | 0 |
| 6231 | 67 × 93 = 6231, so it is a multiple of 67. | 0 |
| 6298 | 67 × 94 = 6298, so it is a multiple of 67. | 0 |
| 6365 | 67 × 95 = 6365, so it is a multiple of 67. | 0 |
| 6432 | 67 × 96 = 6432, so it is a multiple of 67. | 0 |
| 6499 | 67 × 97 = 6499, so it is a multiple of 67. | 0 |
| 6566 | 67 × 98 = 6566, so it is a multiple of 67. | 0 |
| 6633 | 67 × 99 = 6633, so it is a multiple of 67. | 0 |
| 6700 | 67 × 100 = 6700, so it is a multiple of 67. | 0 |
Read More About Multiples of 67
Important Notes
- Even Numbers: All multiples of 67 are not necessarily even numbers.
- Divisibility: A number is a multiple of 67 if it can be divided by 67 with no remainder.
- Factors: Multiples of 67 have 67 as one of their factors.
- Infinite Sequence: There are infinitely many multiples of 67, extending indefinitely as 67, 134, 201, 268, 335, and so on.
- Arithmetic Pattern: The difference between consecutive multiples of 67 is always 67.
Examples on Multiples of 67
Simple Multiples
134: 67 × 2 = 134
335: 67 × 5 = 335
536: 67 × 8 = 536
Larger Multiples
3350: 67 × 50 = 3350
6700: 67 × 100 = 6700
13400: 67 × 200 = 13400
Real-Life Examples
Time: 4020 seconds in 67 minutes is a multiple of 67 because 67 × 60 = 4020.
Money: 670 cents (or $6.70) is a multiple of 67 because 67 × 10 = 670.
Measurements: 2412 inches in 67 yards is a multiple of 67 because 67 × 36 = 2412.
Practical Examples of Multiples of 67
- A football match lasts 4020 seconds. This is a multiple of 67 because 67 × 60 = 4020.
- Buying 67 packs of gum, each containing 5 pieces, results in 335 pieces of gum. This is calculated as 67 × 5 = 335.
- If a car travels at 67 miles per hour, it covers 134 miles in 2 hours. This is because 67 × 2 = 134.
- A classroom with 67 rows of chairs, each row having 10 chairs, contains 670 chairs. This results from 67 × 10 = 670.
- Baking 67 batches of cookies, with each batch using 4 eggs, requires 268 eggs. This demonstrates that 67 × 4 = 268.
Practical Applications
Counting by Sixty-Sevens: When counting by sixty-sevens (67, 134, 201, 268…), you are listing the multiples of 67.
Even Numbers: Any number that is a multiple of 67, such as 134 or 201, can be divided evenly by 67.
Is 100 a multiple of 67?
No, 100 is not a multiple of 67.
What is the 20th multiple of 67?
The 20th multiple of 67 is 1340 (67 × 20).
How are multiples of 67 useful in real life?
Multiples of 67 can be useful in time calculations, packaging, and measurements, among other applications.
Is 536 a multiple of 67?
Yes, 536 is a multiple of 67 (67 × 8).
What pattern do multiples of 67 follow?
Multiples of 67 increase by 67 each time (e.g., 67, 134, 201, 268).
Can multiples of 67 be odd numbers?
Yes, multiples of 67 can be odd numbers.
Is 804 a multiple of 67?
Yes, 804 is a multiple of 67 (67 × 12).
How can I list multiples of 67?
To list multiples of 67, start with 67 and keep adding 67 to the previous number.
What is the 50th multiple of 67?
The 50th multiple of 67 is 3350 (67 × 50).
Is there a finite number of multiples of 67?
No, there are infinitely many multiples of 67.
Is 1340 a multiple of 67?
Yes, 1340 is a multiple of 67 (67 × 20).
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Practice Test
Which of the following is a multiple of 67?
67
134
201
All of the above
of 10
What is the multiple of 67 that comes immediately after 134?
201
268
335
402
of 10
Which number is not a multiple of 67?
67
134
200
268
of 10
What is the result of adding the first three multiples of 67?
201
268
401
402
of 10
What is the greatest multiple of 67 less than 500?
402
469
534
670
of 10
Which of these numbers is closest to 500 and is a multiple of 67?
335
402
469
534
of 10
How many multiples of 67 are there between 67 and 402?
5
6
7
8
of 10
What is the product of 67 and 4?
268
336
402
468
of 10
What is the sum of the first four multiples of 67?
268
269
402
536
of 10