Rules for factors of a composite number
Is there any rule that the factors of a composite number must be of the form $n^m$, where $n$ is a real number and $m ge 1$?
Example 1: the factors of $4$ are : $2^2, 1^1, 4^1$.
Example 2: The factors of $-4$ are $-2^2, -4^1, -1^1$, and so on.
real-numbers prime-factorization
|
show 2 more comments
Is there any rule that the factors of a composite number must be of the form $n^m$, where $n$ is a real number and $m ge 1$?
Example 1: the factors of $4$ are : $2^2, 1^1, 4^1$.
Example 2: The factors of $-4$ are $-2^2, -4^1, -1^1$, and so on.
real-numbers prime-factorization
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
@Billy I have edited!
– pro neon
Jun 12 at 6:53
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
1
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56
|
show 2 more comments
Is there any rule that the factors of a composite number must be of the form $n^m$, where $n$ is a real number and $m ge 1$?
Example 1: the factors of $4$ are : $2^2, 1^1, 4^1$.
Example 2: The factors of $-4$ are $-2^2, -4^1, -1^1$, and so on.
real-numbers prime-factorization
Is there any rule that the factors of a composite number must be of the form $n^m$, where $n$ is a real number and $m ge 1$?
Example 1: the factors of $4$ are : $2^2, 1^1, 4^1$.
Example 2: The factors of $-4$ are $-2^2, -4^1, -1^1$, and so on.
real-numbers prime-factorization
real-numbers prime-factorization
edited Nov 22 at 13:38
Klangen
1,50611332
1,50611332
asked Jun 12 at 6:44
pro neon
1305
1305
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
@Billy I have edited!
– pro neon
Jun 12 at 6:53
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
1
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56
|
show 2 more comments
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
@Billy I have edited!
– pro neon
Jun 12 at 6:53
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
1
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
@Billy I have edited!
– pro neon
Jun 12 at 6:53
@Billy I have edited!
– pro neon
Jun 12 at 6:53
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
1
1
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56
|
show 2 more comments
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2816609%2frules-for-factors-of-a-composite-number%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2816609%2frules-for-factors-of-a-composite-number%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
I'm not sure I completely understand your question. Can you give us a couple of examples of what you mean?
– Billy
Jun 12 at 6:45
@Billy I have edited!
– pro neon
Jun 12 at 6:53
Well, first of all, since we're talking about factors, $n$ should be an integer, not a real number. Second, when you say the factors of $4$ are $2^2,1^1,4^1$, what does that really mean? The prime factorisation of $4$ is $2cdot2$, which can also be written as $2^2$ if you want (but it's not necessary). The factors of $4$ are $1,2$ and $4$. I don't know what else you could mean.
– Arthur
Jun 12 at 7:15
If $n$ is a factor, you can always write it in the form $n^m$ by setting $m=1$. This doesn't seem to get you anywhere, though.
– saulspatz
Jun 12 at 8:06
1
You could say that $4$ has a factor of $5^0$, but it's kindof pointless. So we don't do that. So yes, we usually require the exponent to be at least $1$.
– Arthur
Jun 12 at 11:56