Time for division!
Number Theory
Level
pending
A number N leaves remainder 7 on being divided by 8, 6 on being divided by 7, 5 on being divided by 6 and so on until 1 on being divided by 2. Find N such that 7000< N <8000
7999
No solution
7559
7255
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1 solution
Here 8 - 7 = 1, 7 - 6 = 1, 6 - 5 = 1 ,...., 2 - 1 = 1 So required no = k{LCM(8,7,6,5,4,3,2) - 1 } (k is natural no) = 840 - 1 =839 Multiple of 840 between 7000 and 8000 is 7560. Thus, N = 7560 - 1 = 7559