ConvertOnline

Image

Audio

Video

Document

Color

1. Convert Online
2. Mathematics
3. Arithmetic
4. Factors of a Number

{
  "topic": "factors-of-number",
  "input_types": [
    "int"
  ],
  "input_labels": [
    "n"
  ],
  "input_values": [
    "12"
  ],
  "type": "Calculate",
  "title": "Factors of a Number",
  "category": "Arithmetic",
  "function": "function myFunc(arr) {\n        let n = arr[0];\n        if (n <= 0) {\n          return \"Please enter a positive integer.\";\n        }\n      \n        const factors = [];\n        for (let i = 1; i <= n; i++) {\n          if (n % i === 0) {\n            factors.push(i);\n          }\n        }\n      \n        return factors.join(\", \");\n      }",
  "op_label": "Factors",
  "explanation": "The factor of a number is an integer that divides the given number without leaving a remainder. A given number can have one or more factors.",
  "content": "<h2>Finding the Factors of a Number</h2>\n<p>The factors of a number are the integers that divide the given number exactly, without leaving a remainder. Every positive integer has at least two factors: 1 and the number itself. However, many numbers have additional factors as well.</p>\n<p>To find the factors of a number, we test each integer from 1 up to the number itself to see if it divides the number with no remainder. If it does, that integer is a factor of the number. If it does not, then that integer is not a factor.</p>\n\n<h2>Examples</h2>\n<p>Let’s explore some examples to understand how we can find the factors of a given number.</p>\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> Find the factors of 12.</h3><h4 class=\"answer\">Answer</h4>\n<p>First, we identify the given number:</p>\n<p><b>Given:</b></p><ul><li><b>n</b> = 12</li></ul>\n<p>Next, we check each integer from 1 to 12 to see if it divides 12 without leaving a remainder:</p>\n<p><b>Steps:</b></p><ul><li>1 divides 12: 12 % 1 = 0 → Factor</li>\n<li>2 divides 12: 12 % 2 = 0 → Factor</li>\n<li>3 divides 12: 12 % 3 = 0 → Factor</li>\n<li>4 divides 12: 12 % 4 = 0 → Factor</li>\n<li>5 does not divide 12: 12 % 5 ≠ 0 → Not a Factor</li>\n<li>6 divides 12: 12 % 6 = 0 → Factor</li>\n<li>7 does not divide 12: 12 % 7 ≠ 0 → Not a Factor</li>\n<li>8 does not divide 12: 12 % 8 ≠ 0 → Not a Factor</li>\n<li>9 does not divide 12: 12 % 9 ≠ 0 → Not a Factor</li>\n<li>10 does not divide 12: 12 % 10 ≠ 0 → Not a Factor</li>\n<li>11 does not divide 12: 12 % 11 ≠ 0 → Not a Factor</li>\n<li>12 divides 12: 12 % 12 = 0 → Factor</li></ul>\n<p>The integers 1, 2, 3, 4, 6, and 12 all divide 12 exactly, so they are factors of 12. The remaining numbers are not factors.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The factors of 12 are: 1, 2, 3, 4, 6, 12.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> Find the factors of 28.</h3><h4 class=\"answer\">Answer</h4>\n<p>We start by identifying the number:</p>\n<p><b>Given:</b></p><ul><li><b>n</b> = 28</li></ul>\n<p>We then check each integer from 1 to 28 to see if it divides 28 without leaving a remainder:</p>\n<p><b>Steps:</b></p><ul><li>1 divides 28: 28 % 1 = 0 → Factor</li>\n<li>2 divides 28: 28 % 2 = 0 → Factor</li>\n<li>3 does not divide 28: 28 % 3 ≠ 0 → Not a Factor</li>\n<li>4 divides 28: 28 % 4 = 0 → Factor</li>\n<li>5 does not divide 28: 28 % 5 ≠ 0 → Not a Factor</li>\n<li>6 does not divide 28: 28 % 6 ≠ 0 → Not a Factor</li>\n<li>7 divides 28: 28 % 7 = 0 → Factor</li>\n<li>8 does not divide 28: 28 % 8 ≠ 0 → Not a Factor</li>\n<li>9 does not divide 28: 28 % 9 ≠ 0 → Not a Factor</li>\n<li>10 does not divide 28: 28 % 10 ≠ 0 → Not a Factor</li>\n<li>11 does not divide 28: 28 % 11 ≠ 0 → Not a Factor</li>\n<li>12 does not divide 28: 28 % 12 ≠ 0 → Not a Factor</li>\n<li>13 does not divide 28: 28 % 13 ≠ 0 → Not a Factor</li>\n<li>14 divides 28: 28 % 14 = 0 → Factor</li>\n<li>15 does not divide 28: 28 % 15 ≠ 0 → Not a Factor</li>\n<li>16 does not divide 28: 28 % 16 ≠ 0 → Not a Factor</li>\n<li>17 does not divide 28: 28 % 17 ≠ 0 → Not a Factor</li>\n<li>18 does not divide 28: 28 % 18 ≠ 0 → Not a Factor</li>\n<li>19 does not divide 28: 28 % 19 ≠ 0 → Not a Factor</li>\n<li>20 does not divide 28: 28 % 20 ≠ 0 → Not a Factor</li>\n<li>21 does not divide 28: 28 % 21 ≠ 0 → Not a Factor</li>\n<li>22 does not divide 28: 28 % 22 ≠ 0 → Not a Factor</li>\n<li>23 does not divide 28: 28 % 23 ≠ 0 → Not a Factor</li>\n<li>24 does not divide 28: 28 % 24 ≠ 0 → Not a Factor</li>\n<li>25 does not divide 28: 28 % 25 ≠ 0 → Not a Factor</li>\n<li>26 does not divide 28: 28 % 26 ≠ 0 → Not a Factor</li>\n<li>27 does not divide 28: 28 % 27 ≠ 0 → Not a Factor</li>\n<li>28 divides 28: 28 % 28 = 0 → Factor</li></ul>\n<p>The integers 1, 2, 4, 7, 14, and 28 all divide 28 exactly, so they are factors of 28. The remaining numbers are not factors.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The factors of 28 are: 1, 2, 4, 7, 14, 28.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> Determine the factors of 15.</h3><h4 class=\"answer\">Answer</h4>\n<p>We begin by identifying the number:</p>\n<p><b>Given:</b></p><ul><li><b>n</b> = 15</li></ul>\n<p>Next, we check each integer from 1 to 15 to see if it divides 15 without leaving a remainder:</p>\n<p><b>Steps:</b></p><ul><li>1 divides 15: 15 % 1 = 0 → Factor</li>\n<li>2 does not divide 15: 15 % 2 ≠ 0 → Not a Factor</li>\n<li>3 divides 15: 15 % 3 = 0 → Factor</li>\n<li>4 does not divide 15: 15 % 4 ≠ 0 → Not a Factor</li>\n<li>5 divides 15: 15 % 5 = 0 → Factor</li>\n<li>6 does not divide 15: 15 % 6 ≠ 0 → Not a Factor</li>\n<li>7 does not divide 15: 15 % 7 ≠ 0 → Not a Factor</li>\n<li>8 does not divide 15: 15 % 8 ≠ 0 → Not a Factor</li>\n<li>9 does not divide 15: 15 % 9 ≠ 0 → Not a Factor</li>\n<li>10 does not divide 15: 15 % 10 ≠ 0 → Not a Factor</li>\n<li>11 does not divide 15: 15 % 11 ≠ 0 → Not a Factor</li>\n<li>12 does not divide 15: 15 % 12 ≠ 0 → Not a Factor</li>\n<li>13 does not divide 15: 15 % 13 ≠ 0 → Not a Factor</li>\n<li>14 does not divide 15: 15 % 14 ≠ 0 → Not a Factor</li>\n<li>15 divides 15: 15 % 15 = 0 → Factor</li></ul>\n<p>The integers 1, 3, 5, and 15 all divide 15 exactly, so they are factors of 15. The remaining numbers are not factors.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The factors of 15 are: 1, 3, 5, 15.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> Find the factors of 20.</h3><h4 class=\"answer\">Answer</h4>\n<p>We start by identifying the number:</p>\n<p><b>Given:</b></p><ul><li><b>n</b> = 20</li></ul>\n<p>We then check each integer from 1 to 20 to determine if it divides 20 without leaving a remainder:</p>\n<p><b>Steps:</b></p><ul><li>1 divides 20: 20 % 1 = 0 → Factor</li>\n<li>2 divides 20: 20 % 2 = 0 → Factor</li>\n<li>3 does not divide 20: 20 % 3 ≠ 0 → Not a Factor</li>\n<li>4 divides 20: 20 % 4 = 0 → Factor</li>\n<li>5 divides 20: 20 % 5 = 0 → Factor</li>\n<li>6 does not divide 20: 20 % 6 ≠ 0 → Not a Factor</li>\n<li>7 does not divide 20: 20 % 7 ≠ 0 → Not a Factor</li>\n<li>8 does not divide 20: 20 % 8 ≠ 0 → Not a Factor</li>\n<li>9 does not divide 20: 20 % 9 ≠ 0 → Not a Factor</li>\n<li>10 divides 20: 20 % 10 = 0 → Factor</li>\n<li>11 does not divide 20: 20 % 11 ≠ 0 → Not a Factor</li>\n<li>12 does not divide 20: 20 % 12 ≠ 0 → Not a Factor</li>\n<li>13 does not divide 20: 20 % 13 ≠ 0 → Not a Factor</li>\n<li>14 does not divide 20: 20 % 14 ≠ 0 → Not a Factor</li>\n<li>15 does not divide 20: 20 % 15 ≠ 0 → Not a Factor</li>\n<li>16 does not divide 20: 20 % 16 ≠ 0 → Not a Factor</li>\n<li>17 does not divide 20: 20 % 17 ≠ 0 → Not a Factor</li>\n<li>18 does not divide 20: 20 % 18 ≠ 0 → Not a Factor</li>\n<li>19 does not divide 20: 20 % 19 ≠ 0 → Not a Factor</li>\n<li>20 divides 20: 20 % 20 = 0 → Factor</li></ul>\n<p>The integers 1, 2, 4, 5, 10, and 20 all divide 20 exactly, so they are factors of 20. The remaining numbers are not factors.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The factors of 20 are: 1, 2, 4, 5, 10, 20.</p></div>"
}