Answer:
We know that, a number is divisible by 4, if the number formed by last two digits i.e. tens and ones place digits are divisible by 4. Number is divisible by 8, if the number formed by last three digits i.e. its hundreds, tens and ones place digits are divisible by 8. (a) We have, 572 (i) Divisibility by 4 Number formed by last two digits = 72 On dividing 72 by 4, we get Remainder = 0 \[\because \] 72 is divisible by 4, so 572 is also divisible by 4. \[\frac{\begin{align} & 4\overline{)72(}18 \\ & \,\,\,\,\,\,\,4 \\ \end{align}}{\begin{align} & 32 \\ & \frac{32}{\times } \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits On dividing 572 by 8, we get Remainder \[\ne 0\] \[\therefore \] 572 is not divisible by 8. \[\frac{\begin{align} & 8\overline{)572(}71 \\ & \,\,\,\,\,\,\,56 \\ \end{align}}{\begin{align} & 12 \\ & \frac{8}{4} \\ \end{align}}\] (b) We have, 726352 (i) Divisibility by 4 Number formed by last two digits = 52 On dividing 52 by 4, we get Remainder = 0 \[\because \] 52 is divisible by 4, so 726352 is also divisible by 4. \[\frac{\begin{align} & 4\overline{)52(}13 \\ & \,\,\,\,\,\,\,4 \\ \end{align}}{\begin{align} & \,\,12 \\ & \frac{12}{\underline{\,\,4\,\,\,\,}} \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits = 352 On dividing 352 by 8, we get Remainder = 0 \[\because \] 352 is divisible by 8 \[\therefore \] 726352 is also divisible by 8. \[\frac{\begin{align} & 8\overline{)352(}44 \\ & \,\,\,\,\,\,\,32 \\ \end{align}}{\begin{align} & 32 \\ & \frac{32}{\underline{\,\times \,\,\,\,}} \\ \end{align}}\] (c) We have, 5500 (i) Divisibility by 4 Number formed by last two digits = 00 which is divisible by 4. \[\therefore \] 5500 is divisible by 4 (ii) Divisibility by 8 Number formed by last three digits = 500 On dividing 500 by 8, we get Remainder \[\ne 0\] \[\because \]500 is not divisible by 8 \[\therefore \] 5500 is not divisible by 8. \[\frac{\begin{align} & 8\overline{)500(}62 \\ & \,\,\,\,\,\,\,48 \\ \end{align}}{\begin{align} & 20 \\ & \frac{16}{4} \\ \end{align}}\] (d) We have, 6000 (i) Divisibility by 4 Number formed by last two digits = 00 which is divisible by 4. \[\therefore \]6000 is divisible by 4. (ii) Divisibility by 8 Number formed by last three digits = 000 which is divisible by 8. \[\therefore \]6000 is divisible by 8. (e) We have, 12159 (i) Divisibility by 4 Number formed by last two digits = 59 On dividing 59 by 4, we get Remainder\[\ne 0\] \[\because \]59 is not divisible by 4, so 12159 is not divisible by 4. \[\frac{\begin{align} & 4\overline{)59(}14 \\ & \,\,\,\,\,\,\,4 \\ \end{align}}{\begin{align} & 19 \\ & \frac{16}{3} \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits = 159 On dividing 159 by 8, we get Remainder \[\ne 0\] \[\because \]159 is not divisible by 8, \[\therefore \]12159 is not divisible by 8. \[\frac{\begin{align} & 8\overline{)159(}19 \\ & \,\,\,\,\,\,\,8 \\ \end{align}}{\begin{align} & 79 \\ & \frac{72}{7} \\ \end{align}}\] (f) We have, 14560 (i) Divisibility by 4 Number formed by last two digits = 60 On dividing 60 by 4, we get Remainder = 0 \[\because \] 60 is divisible by 4, so 14560 is also divisible by 4. \[\frac{\begin{align} & 4\overline{)60(}15 \\ & \,\,\,\,\,\,\,4 \\ \end{align}}{\begin{align} & 20 \\ & \frac{20}{\underline{\,\,\times \,\,\,\,\,}} \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits = 560 On dividing 560 by 8, we get Remainder = 0 \[\because \] 560 is divisible by 8. \[\therefore \] 14560 is also divisible by 8. \[\frac{\begin{align} & 8\overline{)560(}70 \\ & \,\,\,\,\,\,\,56 \\ \end{align}}{\begin{align} & 0 \\ & \frac{0}{\times } \\ \end{align}}\] (g) We have, 21084 (i) Divisibility by 4 Number formed by last two digits = 84 On dividing 84 by 4, we get Remainder = 0 \[\because \] 84 is divisible by 4, so 21084 is divisible by 4. \[\frac{\begin{align} & 4\overline{)84(}21 \\ & \,\,\,\,\,\,\,8 \\ \end{align}}{\begin{align} & 4 \\ & \frac{4}{\underline{\times }} \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits = 084 = 84 On dividing 084 by 8, we get Remainder \[\ne 0\] \[\because \] 084 is not divisible by 8. \[\therefore \] 21084 also not divisible by 8. (h) We have, 31795072 (i) Divisibility by 4 Number formed by last two digits = 72 On dividing 72 by 4, we get Remainder = 0 \[\because \]72 is divisible by 4. \[\therefore \]31795072 is also divisible by 4. \[\frac{\begin{align} & 4\overline{)72(}18 \\ & \,\,\,\,\,\,\,4 \\ \end{align}}{\begin{align} & 32 \\ & \frac{32}{\underline{\times }} \\ \end{align}}\] (ii) Divisibility by 8 Number formed by last three digits = 072 = 72 On dividing 072 by 8, we get Remainder = 0 \[\because \] 072 is divisible by 8, so 31795072 is also divisible by 8. \[\frac{8\overline{)72(}9}{\frac{72}{\underline{\times }}}\] (i) We have, 1700 (i) Divisibility by 4 Number formed by last two digits = 00, which is divisible by 4. \[\therefore \] 1700 is also divisible by 4. (ii) Divisibility by 8 Number formed by last three digits = 700 On dividing 700 by 8, we get Remainder \[\ne 0\] \[\because \]700 is not divisible by 8. \[\therefore \]1700 is also not divisible by 8. \[\frac{8\overline{)700(}87}{\frac{64}{\frac{60}{\frac{56}{4}}}}\] (j) We have, 2150 (i) Divisibility by 4 Number formed by last two digits = 50 On dividing 50 by 4, we get Remainder \[\ne 0\] \[\because \] 50 is not divisible by 4, so 2150 is also not divisible by 4. \[\frac{4\overline{)50(}12}{\frac{4}{\frac{10}{\frac{8}{2}}}}\] (ii) Divisibility by 8 Number formed by last three digits = 150 On dividing 150 by 8, we get Remainder \[\ne 0\] \[\because \] 150 is not divisible by 8 \[\therefore \] 2150 is also divisible by 8. \[\frac{8\overline{)150(}18}{\frac{8}{\frac{70}{\frac{64}{6}}}}\]
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