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Concept

Relatively Prime Numbers

Two numbers are relatively prime if they have no common factors except for

1 .

In other words, relatively prime numbers do not have a common divisor other than

1,

in which the numbers can be divided without having a remainder. Relatively prime numbers are also called coprime numbers or mutually prime numbers.

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Properties of Relatively Prime Numbers

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 $2$
$5$ and $14$	$14$	$1, 2, 7, 14$	$\times$	$1$	$✓$	$1$ and $2$
$2$ and $17$	$2$	$1, 2$	$✓$	$1$	$✓$	$2$
$2$ and $17$	$17$	$1, 17$	$✓$	$1$	$✓$	$2$
$7$ and $14$	$7$	$1, 7$	$✓$	$1, 7$	$\times$	$2$
$7$ and $14$	$14$	$1, 2, 7, 14$	$\times$	$1, 7$	$\times$	$2$
$9$ and $10$	$9$	$1, 3, 9$	$\times$	$1$	$✓$	$1$ and $3$
$9$ and $10$	$10$	$1, 2, 5, 10$	$\times$	$1$	$✓$	$1$ and $3$
$6$ and $8$	$6$	$1, 2, 3, 6$	$\times$	$1, 2$	$\times$	$4$
$6$ and $8$	$8$	$1, 2, 4, 8$	$\times$	$1, 2$	$\times$	$4$

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