全國中學(xué)生數(shù)學(xué)競賽數(shù)論部分試題及答案1.若正整數(shù)\(a\)、\(b\)滿足\(a=3b\)，則\(a\)和\(b\)的最大公因數(shù)是（）A.\(a\)B.\(b\)C.\(3\)D.\(ab\)答案：B2.能被\(3\)整除的數(shù)的特征是（）A.各位數(shù)字之和能被\(3\)整除B.個位數(shù)字是\(3\)的倍數(shù)C.奇數(shù)位數(shù)字之和能被\(3\)整除D.偶數(shù)位數(shù)字之和能被\(3\)整除答案：A3.兩個連續(xù)自然數(shù)的積一定是（）A.奇數(shù)B.偶數(shù)C.質(zhì)數(shù)D.合數(shù)答案：B4.一個數(shù)既是\(12\)的因數(shù)，又是\(12\)的倍數(shù)，這個數(shù)是（）A.\(1\)B.\(12\)C.\(24\)D.\(36\)答案：B5.最小的質(zhì)數(shù)與最小的合數(shù)的積是（）A.\(2\)B.\(4\)C.\(6\)D.\(8\)答案：D6.若\(a\)是奇數(shù)，\(b\)是偶數(shù)，則\(a+b\)一定是（）A.奇數(shù)B.偶數(shù)C.質(zhì)數(shù)D.合數(shù)答案：A7.一個數(shù)除以\(5\)余\(3\)，除以\(7\)余\(5\)，這個數(shù)最小是（）A.\(33\)B.\(34\)C.\(35\)D.\(36\)答案：A8.已知\(a\divb=5\)（\(a\)、\(b\)均為非零自然數(shù)），則\(a\)和\(b\)的最小公倍數(shù)是（）A.\(a\)B.\(b\)C.\(5\)D.\(ab\)答案：A9.下列數(shù)中，不是質(zhì)數(shù)的是（）A.\(2\)B.\(9\)C.\(11\)D.\(13\)答案：B10.一個三位數(shù)，個位數(shù)字是\(0\)，百位數(shù)字是\(1\)，十位數(shù)字是\(2\)，這個數(shù)是\(3\)的倍數(shù)嗎？（）A.是B.不是C.不確定D.以上都不對答案：A11.兩個數(shù)的最大公因數(shù)是\(6\)，最小公倍數(shù)是\(36\)，這兩個數(shù)可能是（）A.\(6\)和\(36\)B.\(12\)和\(18\)C.\(18\)和\(24\)D.\(6\)和\(12\)答案：B12.若\(n\)是自然數(shù)，則\(2n+1\)一定是（）A.奇數(shù)B.偶數(shù)C.質(zhì)數(shù)D.合數(shù)答案：A13.一個數(shù)的因數(shù)的個數(shù)是（）A.有限的B.無限的C.不確定D.以上都不對答案：A14.能同時被\(2\)、\(3\)、\(5\)整除的最小三位數(shù)是（）A.\(100\)B.\(102\)C.\(120\)D.\(150\)答案：C15.把\(30\)分解質(zhì)因數(shù)是（）A.\(30=5×6\)B.\(30=2×3×5\)C.\(30=1×2×3×5\)D.\(30=2×15\)答案：B16.一個質(zhì)數(shù)有（）個因數(shù)。A.\(1\)B.\(2\)C.\(3\)D.無數(shù)個答案：B17.兩個質(zhì)數(shù)的和是\(10\)，積是\(21\)，這兩個質(zhì)數(shù)分別是（）A.\(3\)和\(7\)B.\(2\)和\(8\)C.\(4\)和\(6\)D.\(1\)和\(9\)答案：A18.一個數(shù)除以\(8\)余\(5\)，除以\(6\)余\(3\)，這個數(shù)最小是（）A.\(21\)B.\(23\)C.\(25\)D.\(27\)答案：A19.若\(a\)、\(b\)互質(zhì)，則它們的最小公倍數(shù)是（）A.\(a\)B.\(b\)C.\(ab\)D.\(1\)答案：C20.一個數(shù)既是\(48\)的因數(shù)，又是\(6\)的倍數(shù)，這個數(shù)可能是（）A.\(6\)、\(12\)、\(18\)、\(24\)B.\(6\)、\(12\)、\(24\)、\(48\)C.\(12\)、\(18\)、\(24\)、\(36\)D.\(12\)、\(24\)、\(36\)、\(48\)答案：B1.以下哪些數(shù)是\(2\)的倍數(shù)？（）A.\(12\)B.\(15\)C.\(18\)D.\(20\)答案：ACD2.能被\(5\)整除的數(shù)的特征有（）A.個位數(shù)字是\(0\)或\(5\)B.各位數(shù)字之和能被\(5\)整除C.奇數(shù)位數(shù)字之和能被\(5\)整除D.偶數(shù)位數(shù)字之和能被\(5\)整除答案：A3.下列數(shù)中，是質(zhì)數(shù)的有（）A.\(2\)B.\(3\)C.\(5\)D.\(7\)答案：ABCD4.兩個數(shù)的最小公倍數(shù)的求法可能涉及（）A.分解質(zhì)因數(shù)法B.列舉法C.短除法D.直接觀察法答案：ABC5.以下哪些數(shù)是\(3\)的倍數(shù)？（）A.\(123\)B.\(234\)C.\(345\)D.\(456\)答案：ABCD6.一個數(shù)既是\(6\)的倍數(shù)，又是\(8\)的倍數(shù)，這個數(shù)可能是（）A.\(24\)B.\(48\)C.\(72\)D.\(96\)答案：ABCD7.能同時被\(2\)、\(3\)整除的數(shù)的特征是（）A.個位數(shù)字是偶數(shù)B.各位數(shù)字之和能被\(3\)整除C.個位數(shù)字是\(0\)、\(2\)、\(4\)、\(6\)、\(8\)且各位數(shù)字之和能被\(3\)整除D.奇數(shù)位數(shù)字之和能被\(3\)整除且個位數(shù)字是偶數(shù)答案：C8.兩個連續(xù)偶數(shù)的和一定是（）A.奇數(shù)B.偶數(shù)C.是\(a\)的倍數(shù)（設(shè)其中一個偶數(shù)為\(a\)）D.是\(4\)的倍數(shù)答案：BD9.一個數(shù)除以\(4\)余\(1\)，除以\(5\)余\(1\)，這個數(shù)可能是（）A.\(21\)B.\(41\)C.\(61\)D.\(81\)答案：ABCD10