300

300は自然数、また整数において、299の次で301の前の数である。

1. 性質
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300は合成数であり、約数は 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 と 300 である。
約数の和は868。
69番目の過剰数である。1つ前は294、次は304。
約数の和が回文数になる26番目の数である。1つ前は281、次は314。
約数を18個もつ4番目の数である。1つ前は288、次は396。
300 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + … + 23 + 24
24番目の三角数である。1つ前は276、次は325。
三角数が過剰数になる7番目の数である。1つ前は276、次は378。
三角数がハーシャッド数になる13番目の数である。1つ前は210、次は351。
三角数において各位の和も三角数になる19番目の数である。1つ前は276、次は325。
300 = 3 + 21 + 276 = 3 + 66 + 231
3つの異なる三角数の和で表せる17番目の三角数である。1つ前は276、次は325。
84番目のハーシャッド数である。1つ前は288、次は306。
3を基としたとき10番目のハーシャッド数である。1つ前は 210、次は 1002。
各位の和が桁数に等しくなる9番目の数である。1つ前は210、次は1003。
各位の平方和が平方数になる35番目の数である。1つ前は296、次は304。
1 = 0.003… 
逆数が循環小数になる数で循環節が1になる25番目の数である。1つ前は288、次は360。
三角関数では sin 300° = − √overline , cos 300° = 1 , tan 300° = − √3}} 。また 300° = 5π rad であり、300グラード = 270°。
3002 + 1 = 90001 であり、//n//2 + 1 の形で素数を生む49番目の数である。1つ前は284、次は306。
約数の和が300になる数は1個ある。 約数の和1個で表せる61番目の数である。1つ前は296、次は304。
300 = 3 × 10
//n// = 10 のときの 3//n//2}} の値とみたとき1つ前は243、次は363。
//n// = 3 のときの 100//n// の値とみたとき1つ前は200、次は400。
300 = 22}} × 3 × 5
3つの異なる素因数の積で //p//2}} × //q//2}} × //r// の形で表せる3番目の数である。1つ前は252、次は396。
300 = 3 × 4 × 52}} = 44}} + 43}} − 42}} − 4
//n// = 4 のときの //n//4}} + //n//3}} − //n//2}} − //n// の値とみたとき1つ前は96、次は720。
300 = 22}} + 102}} + 142}} = 102}} + 102}} + 10
3つの平方数の和2通りで表せる71番目の数である。1つ前は296、次は301。
300 = 22}} + 102}} + 14
異なる3つの平方数の和1通りで表せる87番目の数である。1つ前は298、次は307。
//n// = 300 のとき //n// と //n// − 1 を並べた数を作ると素数になる。//n// と //n// − 1 を並べた数が素数になる36番目の数である。1つ前は294、次は304。
//n// = 300 のとき //n// と //n// + 1 を並べた数を作ると素数になる。//n// と //n// + 1 を並べた数が素数になる35番目の数である。1つ前は278、次は308。
//n// = 300 のとき //n// と //n// − 1 および //n// と //n// + 1 を並べた数が素数になる8番目の数である。1つ前は270、次は312。例．300299 と 300301 は素数。またこの2つの素数は双子素数である。
300 = 73}} − 72}} + 7 − 1
//n// = 7 のときの //n//3}} − //n//2}} + //n// − 1 の値とみたとき1つ前は185、次は455。
300 = 202}} − 100
//n// = 20 のときの //n//2}} − 100 の値とみたとき1つ前は261、次は341。

2. その他 300 に関連すること
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300の接頭辞：trecenti
年始から300日目は平年では10月27日、閏年では10月26日。
西暦300年
紀元前300年
ローマ帝国の暦では、1年は10箇月で、約300日の構成だった。これは、冬の1月と2月を、「寒いから作物が育たない」として略いたもの。
弁護士の蔑称に「三百代言」。
ボウリングでのパーフェクトスコアは300である。1投目から12投連続でストライクを取ると、1フレームあたり30点が加算され、1ゲームは全10フレームなので 30×10=300 が最高点となる。
300メートル競走は陸上競技種目の一つ。
離婚後300日問題
300〈スリーハンドレッド〉
300勝クラブは300勝を達成した投手の集団。
300系または300形を称するもの。
自動車では排気量などの"車格"を表す数字として車種名に使用される。
メルセデス・ベンツの乗用車の車種名、E300、300SE、300SLなど。
レクサスの乗用車の車種名、SC300。
クライスラーの乗用車の車種名、クライスラー・300。
エアバスA300は世界初の双発ワイドボディ旅客機。座席数300席にちなみ機名が決定された。
三百人委員会は陰謀論で語られる秘密組織。

3. 301 から 399 までの整数
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3.1. 301から320
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301 = 7 × 43、95番目の半素数

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302 = 2 × 151、96番目の半素数

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303 = 3 × 101、97番目の半素数、回文数

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304 = 24 × 19、7番目の原始擬似完全数

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305 = 5 × 61、98番目の半素数

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306 = 2 × 32 × 17、17番目の矩形数、85番目のハーシャッド数

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307 = 素数、17番目の8n + 3型の素数

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308 = 22 × 7 × 11、86番目のハーシャッド数、3連続偶数の平方和

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309 = 3 × 103、99番目の半素数

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310 = 2 × 5 × 31、33番目の楔数

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311 = 素数、エマープ、双子素数、数字を入れかえた131も素数

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312 = 23 × 3 × 13、87番目のハーシャッド数

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313 = 素数、双子素数、回文数、回文素数、数字を入れかえた331も素数

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314 = 2 × 157、100番目の半素数

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315 = 32 × 5 × 7、88番目のハーシャッド数

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316 = 22 × 79

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317 = 素数、4番目のレピュニット素数R317

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318 = 2 × 3 × 53、34番目の楔数

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319 = 11 × 29、12番目のスミス数、101番目の半素数

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320 = 26 × 5、89番目のハーシャッド数

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3.2. 321から340
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321 = 3 × 107、102番目の半素数

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322 = 2 × 7 × 23、90番目のハーシャッド数、12番目のリュカ数、35番目の楔数

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323 = 17 × 19、103番目の半素数、回文数

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324 = 22 × 34、平方数182、91番目のハーシャッド数

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325 = 52 × 13、25番目の三角数、13番目の六角数

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326 = 2 × 163、104番目の半素数

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327 = 3 × 109、105番目の半素数、11番目の完全トーティエント数

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328 = 23 × 41、最初から15個の連続した素数の和

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329 = 7 × 47、106番目の半素数

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330 = 2 × 3 × 5 × 11、92番目のハーシャッド数、15番目の五角数、8番目の五胞体数

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331 = 素数、19番目のスーパー素数、18番目の8n + 3型の素数

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332 = 22 × 83

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333 = 32 × 37、回文数、93番目のハーシャッド数

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334 = 2 × 167、107番目の半素数

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335 = 5 × 67、108番目の半素数

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336 = 24 × 3 × 7、高度合成数、94番目のハーシャッド数

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337 = 素数、エマープ、32番目の4n + 1型の素数、32番目の3n + 1型の素数、14番目の8n + 1型の素数、6番目の24n + 1型の素数、8番目の六芒星数

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338 = 2 × 132

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339 = 3 × 113、109番目の半素数

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340 = 22 × 5 × 17、4の累乗和

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3.3. 341から360
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341 = 11 × 31、110番目の半素数

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342 = 2 × 32 × 19、18番目の矩形数、12番目の七角数、95番目のハーシャッド数

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343 = 73、立方数、10番目のフリードマン数、2番目のナイスフリードマン数、回文数

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344 = 23 × 43、4連続偶数の平方和

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345 = 3 × 5 × 23、36番目の楔数

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346 = 2 × 173、13番目のスミス数、111番目の半素数

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347 = 素数、エマープ、双子素数、13番目の安全素数、19番目の8n + 3型の素数、11番目のフリードマン数

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348 = 22 × 3 × 29

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349 = 素数、双子素数、さよくの語呂合わせ

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350 = 2 × 52 × 7、8番目の原始擬似完全数

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351 = 33 × 13、26番目の三角数、96番目のハーシャッド数

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352 = 25 × 11

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353 = 素数、20番目のスーパー素数、回文数、回文素数

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354 = 2 × 3 × 59、37番目の楔数

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355 = 5 × 71、112番目の半素数、14番目のスミス数

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356 = 22 × 89

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357 = 3 × 7 × 17、38番目の楔数

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358 = 2 × 179、113番目の半素数

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359 = 素数、エマープ、21番目のソフィー・ジェルマン素数、14番目の安全素数、18番目の8n - 1型の素数

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360 = 23 × 32 × 5、高度合成数、97番目のハーシャッド数、双子素数の和

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3.4. 361から380
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361 = 192、平方数

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362 = 2 × 181、115番目の半素数

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363 = 3 × 112、回文数

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364 = 22 × 7 × 13、12番目の三角錐数、98番目のハーシャッド数、4連続素数の平方の和

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365 = 5 × 73、116番目の半素数、2連続平方の和、3連続平方の和

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366 = 2 × 3 × 61、39番目の楔数、4連続平方数の和

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367 = 素数、21番目のスーパー素数

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368 = 24 × 23、9番目の原始擬似完全数

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369 = 32 × 41

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370 = 2 × 5 × 37、40番目の楔数、99番目のハーシャッド数、4連続三角数の平方和

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371 = 7 × 53、117番目の半素数、3連続奇数の平方和、5連続三角数の平方和

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372 = 22 × 3 × 31、100番目のハーシャッド数

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373 = 素数、数字を入れかえた337、733も素数、回文数、回文素数、5個の連続した素数の和、5個の連続した素数の平方和

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374 = 2 × 11 × 17、41番目の楔数

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375 = 3 × 53、101番目のハーシャッド数、最初から11個の連続したフィボナッチ数列の和

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376 = 23 × 47、16番目の五角数

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377 = 13 × 29、14番目のフィボナッチ数、118番目の半素数、最初の6個の素数の2乗の総和

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378 = 2 × 33 × 7、102番目のハーシャッド数、27番目の三角数、14番目の六角数、15番目のスミス数

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379 = 素数、20番目の8n + 3型の素数

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380 = 22 × 5 × 19、19番目の矩形数、最初から19個の連続した偶数の和

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3.5. 381から399
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381 = 3 × 127、119番目の半素数、最初から16個の素数の総和

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382 = 2 × 191、120番目の半素数、16番目のスミス数

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383 = 素数、15番目の安全素数、回文数、回文素数

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384 = 27 × 3、1桁の偶数の総乗、双子素数の和

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385 = 5 × 7 × 11、10番目の四角錐数、42番目の楔数

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386 = 2 × 193、121番目の半素数

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387 = 32 × 43

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388 = 22 × 97

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389 = 素数、エマープ、入れ替えた839も素数

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390 = 2 × 3 × 5 × 13

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391 = 17 × 23、122番目の半素数、17番目のスミス数

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392 = 23 × 72、5番目のアキレス数、103番目のハーシャッド数

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393 = 3 × 131、123番目の半素数、回文数

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394 = 2 × 197、124番目の半素数

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395 = 5 × 79、125番目の半素数

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396 = 22 × 32 × 11、104番目のハーシャッド数

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397 = 素数、8番目のキュバン素数、12番目の中央六角数、数字を入れかえた379、739、937も素数

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398 = 2 × 199、126番目の半素数

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399 = 3 × 7 × 19、43番目の楔数、105番目のハーシャッド数、7の累乗和

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4. 関連項目
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数に関する記事の一覧
100 200 300 400 500 600 700 800 900 1000
名数一覧
日本三百名山
300年=3世紀最後の年
//斜体//で表した数は素数である。