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119 lines
3.7 KiB
Text
119 lines
3.7 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Unit 1: Factors and multiples"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Understanding Factor Pairs\n",
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"\n",
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"> [Link to lesson](https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-factors-mult/v/understanding-factor-pairs).\n",
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"\n",
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"**Write a program that finds all the factor pairs for a given number $n$.**\n",
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"\n",
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"- Do not repeat any pairs (e.g., consider `(2, 8)` and `(8, 2)` as the same).\n",
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"- Assume that $n$ is a positive integer greater than or equal to 1 ($n \\in \\mathbb{Z}^+$).\n",
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"\n",
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"For example for $n = 16$, the output of `get_factor_pairs(16)` may be:\n",
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"\n",
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"```\n",
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"{(1, 16), (2, 8), (4, 4)}\n",
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"```\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_factor_pairs(n: int) -> set:\n",
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" factor_pairs: set = set()\n",
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" for i in range(1, n + 1):\n",
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" dividend: int = n\n",
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" divisor: int = i\n",
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" quotient: int = int(dividend / divisor)\n",
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" remainder: int = dividend % divisor\n",
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" if remainder == 0 and (quotient, divisor) not in factor_pairs:\n",
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" factor_pairs.add((divisor, quotient))\n",
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" return factor_pairs\n",
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"\n",
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"assert get_factor_pairs(1) == {(1, 1)}\n",
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"assert get_factor_pairs(15) == {(1, 15), (3, 5)}\n",
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"assert get_factor_pairs(16) == {(1, 16), (2, 8), (4, 4)}\n",
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"assert get_factor_pairs(21) == {(1, 21), (3, 7)}\n",
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"assert get_factor_pairs(26) == {(1, 26), (2, 13)}\n",
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"assert get_factor_pairs(30) == {(1, 30), (2, 15), (3, 10), (5, 6)}\n",
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"assert get_factor_pairs(40) == {(1, 40), (2, 20), (4, 10), (5, 8)}\n",
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"assert get_factor_pairs(42) == {(1, 42), (2, 21), (3, 14), (6, 7)}\n",
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"assert get_factor_pairs(66) == {(1, 66), (2, 33), (3, 22), (6, 11)}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Finding factors of a number\n",
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"\n",
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"> [Link to lesson](https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-factors-mult/v/finding-factors-of-a-number).\n",
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"\n",
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"**Write a program that finds all the factors of a given number $n$.** Assume that $n$ is a positive integer greater than or equal to 1 ($n \\in \\mathbb{Z}^+$).\n",
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"\n",
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"For example for $n = 16$, the output of `get_factors(16)` may be:\n",
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"\n",
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"```\n",
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"{1, 2, 4, 8, 16}\n",
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"```"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_factors(n: int) -> set:\n",
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" factors: set = set()\n",
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" for i in range(1, n + 1):\n",
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" dividend: int = n\n",
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" divisor: int = i\n",
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" quotient: int = int(n / i)\n",
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" remainder: int = n % i\n",
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" if remainder == 0:\n",
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" factors.add(quotient)\n",
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" return factors\n",
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"\n",
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"assert get_factors(16) == {1, 2, 4, 8, 16}\n",
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"assert get_factors(120) == {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "venv",
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"language": "python",
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"name": "python3"
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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