Grade

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Mathematics Undergraduate

整数の問題です。play2の?がふってある部分について、いまいち何を言ってるのかよく分かりません…。もう少し噛み砕いて教えて頂くことはできますか?😭😭

77 特別区Ⅰ類20 PLAY 2 最大公約数と最小公倍数の問題 3つの自然数 14, 63, n は、 最大公約数が 7 で、 最小公倍数が882である。 nが300より小さいとき、 自然数nは全部で何個か。 1. 218 2. 318 最大公約数や最小公倍数の性質は理解できたかな? 3. 418 14 = 7 x 2 63=7 n = 7 882 = 7×2×32×7 72×2×32 は300より小さい自然数であることを、しっかり頭に入れて解きましょう。 14,63, n の最大公約数が 7 なので、 n は 7 を約数に持つ、 つまり、7の 倍数ですから、n=7m (mは整数) とおきます。 ×32 4. 518 また、 14 = 7 x 2.63 = 7× 32 ですから、これらを次のように並べ、最 小公倍数が882 = 2 × 32 x 72 になることを考えます。 xm ← -最小公倍数 最小公倍数の 882 は、 14,63, nのすべてで 割り切れる最小の数ですから、これらの数の素因 数 (素数の約数) をすべて含んでいることになり ますね。 しかし、 14, 63 の素因数に 「7」は1つしか ありませんので、最小公倍数 882 の素因数に 「7」 が2つあるということは、nの素因数に 「7」が 2つあることになります。 そうすると、とりあえず、m=7 であれば、 n=7×7となり、 条件を満たすことがわかり ますが、 m には、 その他の 「2×32」の全部ま たは一部が因数に含まれていても、 最小公倍数は 変わりませんので、n は次のような数が考えられ ます。 そうなの?? 5. 618 ない 71882 71126. 2118 319 3 たとえば、 6と9の最小公 倍数 18 は、次のように、 それぞれの素因数をすべて 含む最小の数だよね。 6=2x3 9 = 3×3 18=2×3×3 たとえば、n=7²×2× 3294 とかでも、次の ように素因数は882に含 まれるでしょ!? 14 = 7×2 63 = 7×32 294 = 7²×2×3 882=7²×2×32 m = m m m m m 4 正解

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English Senior High

2を教えてほしいです💦お願いします🙇

英語 ( 70分) 1 次の文章を読んで 1~7の問いに英語で答えなさい。 It's Christmas Eve, December 24, 1914. The night is clear and cold/ Moonlight illuminates the snow/covered land separating the British and German trenches outside a small town in northern France. British military command feeling nervous sends a message to the front lines: it is thought possible the enemy may attack during Christmas or New Year. Extra caution will be maintained during this period. The military command has no idea what's really about to happen. Around seven for eight in the evening/ British soldier Albert Moren blinks in disbelief What's that on the other side? Lights flicker on./ one by one. Lanterns. he sees, and torches, and... Christmas trees? /"Stille Nacht, That's when he hears it - soldiers singing in German/" heilige Nacht." Never before had the Christmas music sounded so beautiful. I shall never forget it," Moren says later. It was one of the highlights of my life. Then, in response, the British soldiers start singing The First Noel." The Germans applaud, and counter by singing "O Tannenbaum." They go back-and-forth for a while, until finally the two enemy camps sing "O Come, All Ye Faithful" in Latin, together. "This was really a most extraordinary thing." soldier Graham Williams later recalled, "two nations both singing the same Christmas music in the middle of a war." Events just north of a small town in western Belgium go further still. From the enemy trenches, Corporal John Ferguson hears Someone call out, asking if they want some tobacco. "Come towards the light," shouts the German. So Ferguson walks out into no-man's land into the field between both armies. "We were soon speaking as if we had known each other for years." he later wrote. "What a sight little groups of Germans and British talking together almost as far as the eye can seel Out of the darkness we could hear laughter and see lighted matches.... Here we were laughing and chatting to men who only a few hours before we were trying to kill!" The next morning. Christmas Day, the bravest of the soldiers again climb out of the trenches. Walking past the barbed wire, they go over to shake hands with the enemy. Then they wave "come on!" to those who'd stayed behind. "We all cheered." remembered soldier Leslie Washington of the Queen's Westminster Rifles. "and then we all came out together like a football crowd." (A Gifts are exchanged. The British offer chocolate, tea and cakes: and the Germans share cigars, sauerkraut and schnapps. They make jokes and take group photographs as though it's a big./happy reunion/ More than one game of football is played./using helmets for goal posts. One match goes 3-2 to the Germans, another goes to the British, 4-1. In northern France/the opposing sides hold a joint burial service. "The Germans formed up on one side." Lieutenant Arthur Pelham- Burn later wrote./"the English on the other, the military officers standing in front, helmets off, heads bowed in respect. As their friends are laid to rest friends killed by enemy bullets - they sing in English "The Lord is My Shepherd" and the same song in German mein Hirt" their voices in unison. "Der Herr That evening, there are Christmas dinner parties up and down the lines. One English soldier finds himself invited into the German held zone to a wine cellar, where he and a soldier from southern Germany pop open a bottle of 1909 French champagne. The men exchange

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