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| Both sides previous revision Previous revision Next revision | Previous revision | ||
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modular:02_primes [2014/01/31 23:44] marje |
modular:02_primes [2014/01/31 23:59] marje |
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| $3675=2^0 \cdot 3^1 \cdot 5^2 \cdot 7^2 $. | $3675=2^0 \cdot 3^1 \cdot 5^2 \cdot 7^2 $. | ||
| - | Note that there can be primes $p_i$ which do not divide $n$ and thus their power $e_i=0$. | + | Note that there can be primes $p_i$ which do not divide $n$ and thus their power $e_i=0$ written to the end of the prime factorisation if needed. |
| <WRAP task> | <WRAP task> | ||
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| $24=2^{\color{blue}3} \cdot 3^{\color{blue}1}$,\\ | $24=2^{\color{blue}3} \cdot 3^{\color{blue}1}$,\\ | ||
| $30=2^{\color{red}1} \cdot 3^{\color{red}1} \cdot 5^{\color{red}1}$,\\ | $30=2^{\color{red}1} \cdot 3^{\color{red}1} \cdot 5^{\color{red}1}$,\\ | ||
| - | since for the prime $2$ the required relation between powers does not hold | + | since for the prime $2$ the required relation between the powers does not hold |
| ^primes |$2$ |$3$ | $5$ | | ^primes |$2$ |$3$ | $5$ | | ||
| Line 78: | Line 78: | ||
| </WRAP> | </WRAP> | ||
| - | This relation between the prime factorisation and divisibility can be used for calculating greatest common divisor and least common multiple. | + | This relation between the prime factorisation and divisibility can be used for calculating the greatest common divisor and the least common multiple. |
| <WRAP nl> | <WRAP nl> | ||
| [[modular:02_gcd]]\\ | [[modular:02_gcd]]\\ | ||
| </WRAP> | </WRAP> | ||