Euclid's Lemma for Prime Divisors/Examples/6

Example of Use of Euclid's Lemma for Prime Divisors

Note that Euclid's Lemma for Prime Divisors does not hold for composite numbers.

For example:

$6 \divides 12 = 3 \times 4$

but:

$6 \nmid 3$ and $6 \nmid 4$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): prime
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prime