How many non-prime integers that lie between 0 and 20 leave either 1 o
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17 Jul 2023, 02:07
Using the dividend divisor relationship, that is, dividend = (Divisor× Quotient) + Remainder, let the positive integer which on dividing by 6 leaves remainder 1 or 2 be n which will be represented as;
𝑛 = \(6 \ell _1 + 1\) and 𝑛 = \(6 \ell _2 + 2\) [\(\ell_1\) and \(\ell_2\) are integer quotient]
𝑛 =\(6 \ell _1 + 1\)
Considering different values of \(\ell_ 1\): 0, 1, 2, 3, …
𝑛 = 1, 7, 13, 19, …
And, 𝑛 = \(6 \ell _2 + 2\) − −−→ 2,8,14 …
Hence, the non-prime integers that lie between 0 and 20 which leaves either 1 or 2 as remainder when divided by 6 will be 1, 8, 14
Ans. is 3