Multiples of 17
Multiples of 17
In mathematics, multiples of 17 are integers obtained by multiplying 17 by other whole numbers. These numbers are part of the integer set and follow the basic principles of multiplication. Multiples of 17 have 17 as one of their divisors, meaning 17 can divide them without leaving a remainder. As factors of these multiples, 17 and the corresponding whole number produce a sequence of numbers that extend infinitely. Understanding multiples of 17 helps in various mathematical concepts, including identifying patterns and solving problems related to divisors and factors.
What are Multiples of 17?
Multiples of 17 are integers obtained by multiplying 17 with any whole number. They are part of the integer set and include numbers like 17, 34, 51, and so on. These multiples have 17 as a divisor, meaning they can be divided by 17 without leaving a remainder.
For example, 34, 68, 119 and 153 are all multiples of 17, 160 is not a multiple of 17 for the following reasons:
| Number | Explanation | Remainder |
|---|---|---|
| 34 | 34÷17 = 2 (Integer result, no remainder) | 0 |
| 68 | 68÷17 = 4 (Integer result, no remainder) | 0 |
| 119 | 119÷17 = 7 (Integer result, no remainder) | 0 |
| 153 | 153÷17 = 9 (Integer result, no remainder) | 0 |
| 160 | 160÷17 = 9.41 (Non-integer result) | 7 |
List of First 100 Multiples of 17 with Remainders
| Number | Calculation | Remainder |
|---|---|---|
| 17 | 17÷17 = 1, so 17 is divisible by 17. | 0 |
| 34 | 34÷17 = 2, so 34 is divisible by 17. | 0 |
| 51 | 51÷17 = 3, so 51 is divisible by 17. | 0 |
| 68 | 68÷17 = 4, so 68 is divisible by 17. | 0 |
| 85 | 85÷17 = 5, so 85 is divisible by 17. | 0 |
| 102 | 102÷17 = 6, so 102 is divisible by 17. | 0 |
| 119 | 119÷17 = 7, so 119 is divisible by 17. | 0 |
| 136 | 136÷17 = 8, so 136 is divisible by 17. | 0 |
| 153 | 153÷17 = 9, so 153 is divisible by 17. | 0 |
| 170 | 170÷17 = 10, so 170 is divisible by 17. | 0 |
| 187 | 187÷17 = 11, so 187 is divisible by 17. | 0 |
| 204 | 204÷17 = 12, so 204 is divisible by 17. | 0 |
| 221 | 221÷17 = 13, so 221 is divisible by 17. | 0 |
| 238 | 238÷17 = 14, so 238 is divisible by 17. | 0 |
| 255 | 255÷17 = 15, so 255 is divisible by 17. | 0 |
| 272 | 272÷17 = 16, so 272 is divisible by 17. | 0 |
| 289 | 289÷17 = 17, so 289 is divisible by 17. | 0 |
| 306 | 306÷17 = 18, so 306 is divisible by 17. | 0 |
| 323 | 323÷17 = 19, so 323 is divisible by 17. | 0 |
| 340 | 340÷17 = 20, so 340 is divisible by 17. | 0 |
| 357 | 357÷17 = 21, so 357 is divisible by 17. | 0 |
| 374 | 374÷17 = 22, so 374 is divisible by 17. | 0 |
| 391 | 391÷17 = 23, so 391 is divisible by 17. | 0 |
| 408 | 408÷17 = 24, so 408 is divisible by 17. | 0 |
| 425 | 425÷17 = 25, so 425 is divisible by 17. | 0 |
| 442 | 442÷17 = 26, so 442 is divisible by 17. | 0 |
| 459 | 459÷17 = 27, so 459 is divisible by 17. | 0 |
| 476 | 476÷17 = 28, so 476 is divisible by 17. | 0 |
| 493 | 493÷17 = 29, so 493 is divisible by 17. | 0 |
| 510 | 510÷17 = 30, so 510 is divisible by 17. | 0 |
| 527 | 527÷17 = 31, so 527 is divisible by 17. | 0 |
| 544 | 544÷17 = 32, so 544 is divisible by 17. | 0 |
| 561 | 561÷17 = 33, so 561 is divisible by 17. | 0 |
| 578 | 578÷17 = 34, so 578 is divisible by 17. | 0 |
| 595 | 595÷17 = 35, so 595 is divisible by 17. | 0 |
| 612 | 612÷17 = 36, so 612 is divisible by 17. | 0 |
| 629 | 629÷17 = 37, so 629 is divisible by 17. | 0 |
| 646 | 646÷17 = 38, so 646 is divisible by 17. | 0 |
| 663 | 663÷17 = 39, so 663 is divisible by 17. | 0 |
| 680 | 680÷17 = 40, so 680 is divisible by 17. | 0 |
| 697 | 697÷17 = 41, so 697 is divisible by 17. | 0 |
| 714 | 714÷17 = 42, so 714 is divisible by 17. | 0 |
| 731 | 731÷17 = 43, so 731 is divisible by 17. | 0 |
| 748 | 748÷17 = 44, so 748 is divisible by 17. | 0 |
| 765 | 765÷17 = 45, so 765 is divisible by 17. | 0 |
| 782 | 782÷17 = 46, so 782 is divisible by 17. | 0 |
| 799 | 799÷17 = 47, so 799 is divisible by 17. | 0 |
| 816 | 816÷17 = 48, so 816 is divisible by 17. | 0 |
| 833 | 833÷17 = 49, so 833 is divisible by 17. | 0 |
| 850 | 850÷17 = 50, so 850 is divisible by 17. | 0 |
| 867 | 867÷17 = 51, so 867 is divisible by 17. | 0 |
| 884 | 884÷17 = 52, so 884 is divisible by 17. | 0 |
| 901 | 901÷17 = 53, so 901 is divisible by 17. | 0 |
| 918 | 918÷17 = 54, so 918 is divisible by 17. | 0 |
| 935 | 935÷17 = 55, so 935 is divisible by 17. | 0 |
| 952 | 952÷17 = 56, so 952 is divisible by 17. | 0 |
| 969 | 969÷17 = 57, so 969 is divisible by 17. | 0 |
| 986 | 986÷17 = 58, so 986 is divisible by 17. | 0 |
| 1003 | 1003÷17 = 59, so 1003 is divisible by 17. | 0 |
| 1020 | 1020÷17 = 60, so 1020 is divisible by 17. | 0 |
| 1037 | 1037÷17 = 61, so 1037 is divisible by 17. | 0 |
| 1054 | 1054÷17 = 62, so 1054 is divisible by 17. | 0 |
| 1071 | 1071÷17 = 63, so 1071 is divisible by 17. | 0 |
| 1088 | 1088÷17 = 64, so 1088 is divisible by 17. | 0 |
| 1105 | 1105÷17 = 65, so 1105 is divisible by 17. | 0 |
| 1122 | 1122÷17 = 66, so 1122 is divisible by 17. | 0 |
| 1139 | 1139÷17 = 67, so 1139 is divisible by 17. | 0 |
| 1156 | 1156÷17 = 68, so 1156 is divisible by 17. | 0 |
| 1173 | 1173÷17 = 69, so 1173 is divisible by 17. | 0 |
| 1190 | 1190÷17 = 70, so 1190 is divisible by 17. | 0 |
| 1207 | 1207÷17 = 71, so 1207 is divisible by 17. | 0 |
| 1224 | 1224÷17 = 72, so 1224 is divisible by 17. | 0 |
| 1241 | 1241÷17 = 73, so 1241 is divisible by 17. | 0 |
| 1258 | 1258÷17 = 74, so 1258 is divisible by 17. | 0 |
| 1275 | 1275÷17 = 75, so 1275 is divisible by 17. | 0 |
| 1292 | 1292÷17 = 76, so 1292 is divisible by 17. | 0 |
| 1309 | 1309÷17 = 77, so 1309 is divisible by 17. | 0 |
| 1326 | 1326÷17 = 78, so 1326 is divisible by 17. | 0 |
| 1343 | 1343÷17 = 79, so 1343 is divisible by 17. | 0 |
| 1360 | 1360÷17 = 80, so 1360 is divisible by 17. | 0 |
| 1377 | 1377÷17 = 81, so 1377 is divisible by 17. | 0 |
| 1394 | 1394÷17 = 82, so 1394 is divisible by 17. | 0 |
| 1411 | 1411÷17 = 83, so 1411 is divisible by 17. | 0 |
| 1428 | 1428÷17 = 84, so 1428 is divisible by 17. | 0 |
| 1445 | 1445÷17 = 85, so 1445 is divisible by 17. | 0 |
| 1462 | 1462÷17 = 86, so 1462 is divisible by 17. | 0 |
| 1479 | 1479÷17 = 87, so 1479 is divisible by 17. | 0 |
| 1496 | 1496÷17 = 88, so 1496 is divisible by 17. | 0 |
| 1513 | 1513÷17 = 89, so 1513 is divisible by 17. | 0 |
| 1530 | 1530÷17 = 90, so 1530 is divisible by 17. | 0 |
| 1547 | 1547÷17 = 91, so 1547 is divisible by 17. | 0 |
| 1564 | 1564÷17 = 92, so 1564 is divisible by 17. | 0 |
| 1581 | 1581÷17 = 93, so 1581 is divisible by 17. | 0 |
| 1598 | 1598÷17 = 94, so 1598 is divisible by 17. | 0 |
| 1615 | 1615÷17 = 95, so 1615 is divisible by 17. | 0 |
| 1632 | 1632÷17 = 96, so 1632 is divisible by 17. | 0 |
| 1649 | 1649÷17 = 97, so 1649 is divisible by 17. | 0 |
| 1666 | 1666÷17 = 98, so 1666 is divisible by 17. | 0 |
| 1683 | 1683÷17 = 99, so 1683 is divisible by 17. | 0 |
| 1700 | 1700÷17 = 100, so 1700 is divisible by 17. | 0 |
Read More About Multiples of 17
Important Notes
Definition of Multiples:
- A number is a multiple of 17 if it can be divided by 17 without leaving a remainder.
Examples of Multiples of 17:
- Numbers such as 34, 68, 119, and 153 are multiples of 17 because when divided by 17, the result is an integer with no remainder.
Checking for Multiples:
- To determine if a number is a multiple of 17, divide the number by 17 and check if the remainder is 0. If the remainder is not 0, the number is not a multiple of 17.
Non-Multiples Example:
- The number 160 is not a multiple of 17 because 160÷17 = 9.41, resulting in a remainder of 7.
Remainder Importance:
- The remainder when dividing by 17 helps in identifying if a number is a multiple. A remainder of 0 confirms it is a multiple, while any other remainder indicates it is not.
Examples on Multiples of 17
Example 1: 85
- Calculation: 85÷17 = 5
- Explanation: 85 is a multiple of 17 because it divides evenly, resulting in the integer 5, with no remainder.
Example 2: 204
- Calculation: 204÷17 = 12
- Explanation: 204 is a multiple of 17 because it divides evenly, resulting in the integer 12, with no remainder.
Example 3: 289
- Calculation: 289÷17 = 17
- Explanation: 289 is a multiple of 17 because it divides evenly, resulting in the integer 17, with no remainder.
FAQs
What is a multiple of 17?
A multiple of 17 is a number that can be divided by 17 without leaving a remainder.
How can you determine if a number is a multiple of 17?
To determine if a number is a multiple of 17, divide the number by 17 and check if the remainder is 0. If the remainder is 0, it is a multiple.
What are the first five multiples of 17?
The first five multiples of 17 are 17, 34, 51, 68, and 85.
Is 153 a multiple of 17?
Yes, 153 is a multiple of 17 because 153÷17 = 9, which is an integer with no remainder.
Is 160 a multiple of 17?
No, 160 is not a multiple of 17 because 160÷17 = 9.41, resulting in a remainder of 7.
Can a negative number be a multiple of 17?
Yes, a negative number can be a multiple of 17. For example, -34 is a multiple of 17 because -34÷17 = -2, an integer with no remainder.
Are all multiples of 17 also multiples of its factors?
Yes, all multiples of 17 are also multiples of its factors, such as 1 and 17 itself.
How can you generate multiples of 17?
You can generate multiples of 17 by multiplying 17 by any integer. For example, 17 x 1 = 17, 17 x 2 = 34, 17 x 3 = 51, and so on.
What is the 10th multiple of 17?
The 10th multiple of 17 is 170 because 17×10 = 170.
Is the sum of two multiples of 17 also a multiple of 17?
Yes, the sum of two multiples of 17 is also a multiple of 17. For example, 34 (17 x 2) + 51 (17 x 3) = 85 (17 x 5).
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