100以内被3整除有哪些数 整除的数有哪些特征
JAVA-\u6c42\u51fa100\u4ee5\u5185\u7684\u6574\u6570\u4e2d\u6240\u6709\u7684\u80fd\u88ab3\u6574\u9664\u7684\u6570\u5b57\u7684\u548cpublic class SumDevideThree {
//\u5224\u65adnum\u662f\u5426\u80fd\u88ab3\u6574\u9664\uff0c\u80fd\u8fd4\u56detrue\uff0c\u4e0d\u80fd\u8fd4\u56defalse
public static boolean isDevideExact(int num){
if(num%3==0)
return true;
return false;
}
//\u6c42\u5c0f\u4e8enumber\u7684\u6240\u6709\u80fd\u88ab3\u6574\u9664\u7684\u6570\u7684\u548c\uff0c\u8fd4\u56de\u503c\u4e3a\u6240\u6c42\u7684\u548c
public static int sumNum(int number){
int sum=0;
for(int i=0;i<number;i++){
if(isDevideExact(i))
sum+=i;
}
return sum;
}
public static void main(String[] args){
System.out.println("100\u4ee5\u5185\u7684\u6574\u6570\u4e2d\u6240\u6709\u80fd\u88ab3\u6574\u9664\u7684\u6570\u7684\u548c\u4e3a\uff1a"+sumNum(100));
}
}
1\u3001\u80fd\u88ab2\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u672b\u4f4d\u662f0\u30012\u30014\u30016\u62168\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab2\u6574\u9664\u3002
2\u3001\u80fd\u88ab3\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\uff081\uff09\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u6570\u5b57\u548c\u80fd\u88ab3\u6574\u9664\uff0c\u5219\u8fd9\u4e2a\u6574\u6570\u80fd\u88ab3\u6574\u9664\u3002
\uff082\uff09\u7531\u76f8\u540c\u7684\u6570\u5b57\u7ec4\u6210\u7684\u4e09\u4f4d\u6570\u3001\u516d\u4f4d\u6570\u3001\u4e5d\u4f4d\u6570\u2026\u2026\u8fd9\u4e9b\u6570\u5b57\u80fd\u88ab3\u6574\u9664\u3002\u5982111\u4ee43\u6574\u9664\u3002
3\u3001\u80fd\u88ab4\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u672b\u5c3e\u4e24\u4f4d\u6570\u80fd\u88ab4\u6574\u9664\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab4\u6574\u9664\u3002
4\u3001\u80fd\u88ab5\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u672b\u4f4d\u662f0\u62165\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab5\u6574\u9664\u3002
5\u3001\u80fd\u88ab6\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u80fd\u88ab2\u548c3\u6574\u9664\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab6\u6574\u9664\u3002
6\u3001\u80fd\u88ab8\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u672b\u5c3e\u4e09\u4f4d\u6570\u80fd\u88ab8\u6574\u9664\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab8\u6574\u9664\u3002
7\u3001\u80fd\u88ab9\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u6570\u5b57\u548c\u80fd\u88ab9\u6574\u9664\uff0c\u5219\u8fd9\u4e2a\u6574\u6570\u80fd\u88ab9\u6574\u9664\u3002
8\u3001\u80fd\u88ab10\u6574\u9664\u7684\u6570\u7684\u7279\u5f81
\u82e5\u4e00\u4e2a\u6574\u6570\u7684\u672b\u4f4d\u662f0\uff0c\u5219\u8fd9\u4e2a\u6570\u80fd\u88ab10\u6574\u9664\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u6574\u9664\u7684\u6027\u8d28
1\u3001\u82e5b|a\uff0cc|a\uff0c\u4e14b\u548cc\u4e92\u8d28\uff0c\u5219bc|a\u3002
2\u3001\u5bf9\u4efb\u610f\u975e\u96f6\u6574\u6570a\uff0c\u00b1a|a=\u00b11\u3002
3\u3001\u82e5a|b\uff0cb|a\uff0c\u5219|a|=|b|\u3002
4\u3001\u5982\u679ca\u80fd\u88abb\u6574\u9664\uff0cc\u662f\u4efb\u610f\u6574\u6570\uff0c\u90a3\u4e48\u79efac\u4e5f\u80fd\u88abb\u6574\u9664\u3002
5\u3001\u5bf9\u4efb\u610f\u6574\u6570a\uff0cb>0\uff0c\u5b58\u5728\u552f\u4e00\u7684\u6570\u5bf9q\uff0cr\uff0c\u4f7fa=bq+r\uff0c\u5176\u4e2d0\u2264r<b\uff0c\u8fd9\u4e2a\u4e8b\u5b9e\u79f0\u4e3a\u5e26\u4f59\u9664\u6cd5\u5b9a\u7406\uff0c\u662f\u6574\u9664\u7406\u8bba\u7684\u57fa\u7840\u3002
所以有100/3=33个数...再加上0共34个
如图，100以内凡是个位数和十位数相加的和是三的倍数的数都可以被三整除
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99
绛旓細3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99 杩欎簺100浠ュ唴鐨勬暟閮借兘琚3鏁撮櫎
绛旓細鎵浠ユ湁100/3=33涓暟...鍐嶅姞涓0鍏34涓
绛旓細78銆81銆84銆87銆90銆93銆96銆99
绛旓細琚3鏁撮櫎鐨勬湁 34涓锛堝寘鎷0鐨勮瘽锛夊悇浣嶆湁3鐨 03 13 23 銆傘傘93 涓鍏10涓 鍗佷綅鏈3鐨 30 31 32 ... 39 涓鍏10涓
绛旓細3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 鎬诲叡33
绛旓細鏂规硶涓锛氬浜庝竴涓暟锛屽彧瑕佸叾鍚勪釜浣嶆暟鐩稿姞鎵寰楃殑鍜岃兘琚3鏁撮櫎锛岄偅涔堣繖涓暟灏辫兘琚3鏁撮櫎锛屽33锛3+3=6锛6鍙互琚3鏁撮櫎锛岄偅涔33鍙互琚3鏁撮櫎銆傛柟娉曚簩锛3鐨勫嶆暟閮藉彲浠ヨ3鏁撮櫎锛岃璁＄畻100浠ュ唴鑳借3鏁撮櫎鐨勬暟鐢3渚濇涔樹互鍚勪釜鏁板嵆鍙,鍒楀紡锛3n锛坣=1銆2銆3...)100浠ュ唴鑳借3鏁撮櫎鐨勬暟鏈夛細3銆9銆12銆15...
绛旓細鑳琚3鏁撮櫎鐨勪竴鍏辨湁33涓細3n n=1,2,...,33; n>33,3n>100 1 3 2 6 3 9 4 12 5 15 6 18 7 21 8 24 9 27 10 30 11 33 12 36 13 39 14 42 15 45 16 48 17 51 18 54 19 57 20 60 21 63 22 ...
绛旓細33涓傛牴鎹綔涓氬府APP鏌ヨ鏄剧ず锛屾暣闄ゆ寚鏁撮櫎鏄寚涓涓暟鑳藉琚彟涓涓暟鏁撮櫎锛屽嵆娌℃湁浣欐暟锛100浠ュ唴鑳借3鏁撮櫎鐨勬暟涓3銆6銆9銆12銆15銆18銆21銆24銆27銆30銆33銆36銆39銆42銆45銆48銆51銆54銆57銆60銆63銆66銆69銆72銆75銆78銆81銆84銆87銆90銆93銆96銆99锛屼竴鍏辨湁33涓
绛旓細姣3涓繛缁殑鏁存暟閲岋紝鍙湁涓涓兘琚暣闄ゃ1銆2銆3...99锛屽繀鐒舵湁99/3=33涓兘琚3鏁撮櫎鐨勬暟銆
绛旓細鐢100闄や互3锛屽緱鍒扮殑鍟嗗氨鏄墍姹傘100/3=33鈥︹1 涓鑸儏鍐典笅锛屾眰涓涓暟琚彟涓涓鏁版暣闄鐨勪釜鏁版椂锛屽氨鐢ㄨ繖涓暟闄や互鍙︿竴涓暟锛屽緱鍑烘潵鐨勫晢灏辨槸鎵姹傜殑涓暟銆傛墍浠100浠ュ唴鑳琚3鏁撮櫎鐨勬暟鏈33涓
