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【素因数分解の例】
6=2×3
【注意】10=2×5 8=23(←2×2×2のように同じ数を3回掛けるときは,23と書く.) 18=2×32(←3×3 のように同じ数を2回掛けるときは,32と書く.)
素因数分解は「素数の積」で表わさなければならないので,次のようにただ単に「積」にしただけでは素因数分解とはいえない.
【与えられた整数Nを素因数分解するには】×間違いの例 12=4×3 (← 4 は素数でない.) ⇒ ○正しくは 12=22×3 ×間違いの例 30=3×10 (← 10 は素数でない.) ⇒ ○正しくは 30=2×3×5
(1) N=pq (p≦q)のように書けるとき,小さい方の因数pは必ず
(2)
(*)の理由
N=pq (p≦q)ならばp×p≦N≦q×q すなわち,p2≦N≦q2です. したがって,
【例】
34を素因数分解するには
52<34<62だから5までの素数で割ってみるとよい.
43を素因数分解するには34=2×17…(答)
62<43<72だから6までの素数,2, 3, 5で割ってみるとよい.
いずれでも割り切れないから,43は素数…(答) |
【問題1】
(1)
48の素因数分解について正しいものをクリックしてください.
24, 16, 12は素数ではないので,これらを使って表した式は素因数分解にはなりません.(初めの3個は不可)
48を小さな素数から何度でも割れる限り2, 3, 5, 7などで割っていきます. 48÷2=24 24÷2=12 12÷2=6 6÷2=3 以上により,48=24×3…(答) |
(2)
61の素因数分解について正しいものをしてください. |
(3)
60の素因数分解について正しいものをしてください.
6, 10は素数ではないので,これらを使って表した式は素因数分解にはなりません.(初め選択肢は不可)
72<60<82すなわち 60÷2=30 30÷2=15 15÷3=5 ゆえに,60=22×3×5…(答) |
(4)
87の素因数分解について正しいものをしてください. |
【問題2】
(1)
108の素因数分解について正しいものをクリックしてください. |
(2)
127の素因数分解について正しいものをクリックしてください.
112<127<122すなわち
ところが,2, 3, 5, 7, 11のいずれでも割り切れないから127は素数…(答) |
(3)
123の素因数分解について正しいものをクリックしてください.
112<123<122すなわち
ところで,3の倍数の見分け方というのがあって,各位の数を足したときに3で割り切れたら3の倍数になる.
123÷3=411+2+3=6で6は3で割り切れるから,元の数123も3で割り切れるはずになっている. 123=3×41…(答) |
(4)
149の素因数分解について正しいものをクリックしてください.
122<149<132すなわち
ところが,2, 3, 5, 7, 11のいずれでも割り切れないから149は素数…(答) |
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