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Concept

Here are some properties of relatively prime numbers.

- Relatively prime numbers are not necessarily prime numbers.
- Any prime number is relatively prime with any number except the multiples of the prime number.
- Consecutive numbers are relatively prime.
- Two even numbers are never relatively prime because they have, at least, the common factors of $1$ and $2.$

The following table shows some examples of relatively prime numbers depending on their properties.

Number | Factors | Prime? | Common Factors | Relatively Prime? | Property Number | |
---|---|---|---|---|---|---|

$5$ and $14$ | $5$ | $1,5$ | $✓$ | $1$ | $✓$ | $1$ and $2$ |

$14$ | $1,2,7,14$ | $×$ | ||||

$2$ and $17$ | $2$ | $1,2$ | $✓$ | $1$ | $✓$ | $2$ |

$17$ | $1,17$ | $✓$ | ||||

$7$ and $14$ | $7$ | $1,7$ | $✓$ | $1,7$ | $×$ | $2$ |

$14$ | $1,2,7,14$ | $×$ | ||||

$9$ and $10$ | $9$ | $1,3,9$ | $×$ | $1$ | $✓$ | $1$ and $3$ |

$10$ | $1,2,5,10$ | $×$ | ||||

$6$ and $8$ | $6$ | $1,2,3,6$ | $×$ | $1,2$ | $×$ | $4$ |

$8$ | $1,2,4,8$ | $×$ |

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