# Multiples of 17

Created by: Team Maths - Examples.com, Last Updated: May 23, 2024

## 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.

Prime Factorization of 17: 17 = 17¹ First five multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170.

Table 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.

## 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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