Finding the second factor by employing symmetry
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The factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$. The factors can be organized as such:
$m=1,2,3,4,6,8$, and
$n=72,36,24,18,12,9$.
Knowing the symmetric properties and that the $12$ factors exist. Is there a way to rewrite $n$ as a function of $m$ without actually diving $72$ by $m$? I tried adding and subtracting $m$ and $n$ to find a pattern as to get a clue as to what value the other might be without actually dividing.
prime-factorization
edited Nov 22 at 13:38
Klangen
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
add a comment |
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The factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$. The factors can be organized as such:
$m=1,2,3,4,6,8$, and
$n=72,36,24,18,12,9$.
Knowing the symmetric properties and that the $12$ factors exist. Is there a way to rewrite $n$ as a function of $m$ without actually diving $72$ by $m$? I tried adding and subtracting $m$ and $n$ to find a pattern as to get a clue as to what value the other might be without actually dividing.
prime-factorization
edited Nov 22 at 13:38
Klangen
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$. The factors can be organized as such:
$m=1,2,3,4,6,8$, and
$n=72,36,24,18,12,9$.
Knowing the symmetric properties and that the $12$ factors exist. Is there a way to rewrite $n$ as a function of $m$ without actually diving $72$ by $m$? I tried adding and subtracting $m$ and $n$ to find a pattern as to get a clue as to what value the other might be without actually dividing.
prime-factorization
edited Nov 22 at 13:38
Klangen
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
The factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$. The factors can be organized as such:
$m=1,2,3,4,6,8$, and
$n=72,36,24,18,12,9$.
Knowing the symmetric properties and that the $12$ factors exist. Is there a way to rewrite $n$ as a function of $m$ without actually diving $72$ by $m$? I tried adding and subtracting $m$ and $n$ to find a pattern as to get a clue as to what value the other might be without actually dividing.
prime-factorization
prime-factorization
edited Nov 22 at 13:38
Klangen
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
edited Nov 22 at 13:38
Klangen
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
edited Nov 22 at 13:38
Klangen
1,43711232
edited Nov 22 at 13:38
Klangen
1,43711232
edited Nov 22 at 13:38
Klangen
1,43711232
1,43711232
asked Sep 26 '13 at 15:49
jessica
3881823
asked Sep 26 '13 at 15:49
jessica
3881823
asked Sep 26 '13 at 15:49
jessica
3881823
3881823
The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16
add a comment |
The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16
The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16
The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16
add a comment |
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The defining relation between $m$ and $n$ is $mn=72$. There is no polynomial expression of $m$ in terms of $n$ nor vice-versa because division cannot be done by addition and multiplication.
– lhf
Sep 26 '13 at 16:16