Class 6 Playing with Numbers Exercise 2.5-1

\begin{array}{l} \text {Q1. Test the divisibility of the following numbers by 2 :} \\ (i) \quad 6520 \\ (ii) \quad 984325 \\ (iii) \quad 367314 \\ \\\text {Sol. We know that a natural number is divisible by 2, if its unit digit is 0,2,4,6 or 8.} \\\text {(i) The units digit of 6250 is 0, so it’s divisible by 2.} \\ \text {(ii) The units digit of 984325 is 5, so it is not divisible by 2.} \\\text {(iii) The units digit of 367314 is 4, so its divisible by 2.} \\ \\\text {Q2. Test the divisibility of the following numbers by 3 :} \\ (i) \quad 70335 \\ (ii) \quad 607439 \\ (iii) \quad 9082746 \\ \\\text {Sol. We know that a natural number is divisible by 3, if the sum of its digits is divisible by 3.} \\\text {(i) Sum of the digit of 70335 } = 7 + 0 + 3 + 3 + 5 = 18 \\ \text {Since, 18 is divisible by 3. Therefore, 70335 is divisible by 3.} \\ \\\text {(ii) Sum of the digit of 607439 } = 6 + 0 + 7 + 4 + 3 +9 = 29 \\ \text {Since, 29 is not divisible by 3. Therefore, 607439 is not divisible by 3.} \\ \\\text {(iii) Sum of the digit of 9082746 } = 9 +0 + 8 + 2 + 7 + 4 + 6 = 36 \\ \text {Since, 36 is divisible by 3. Therefore, 9082746 is divisible by 3.} \\ \\\text {Q3. Test the divisibility of the following numbers by 6 : } \\ (i) \quad 7020 \\ (ii) \quad 56423 \\ (iii) \quad 732510 \\ \\\text {Sol. We know that a number is divisible by 6, if its divisible by 2 and 3 both.} \\ \\ \text {(i) Given number } = 7020 \\\text {Its unit digit is 0, so its divisible by 2} \\ \text {Sum of its digit } = 7+0+2+0 = 9 \text { , which is divisible by 3.} \\ \therefore \text {7020 is divisible by 3.} \\ \text {Hence, 7020 is divisible by 6.} \\ \\\text {(ii) Given number } = 56423 \\\text {Its unit digit is 3, so its not divisible by 2} \\\text {Hence, 56423 is not divisible by 6.} \\ \\\text {(iii) Given number } = 732510 \\\text {Its unit digit is 0, so its divisible by 2} \\ \text {Sum of its digit } = 7+3+2+5+1+0 = 18 \text { , which is divisible by 3.} \\ \therefore \text {7073251020 is divisible by 3.} \\ \text {Hence, 732510 is divisible by 6.} \\ \\\text {Q4. Test the divisibility of the following numbers by 4 : } \\ (i) \quad 786532 \\ (ii) \quad 1020531 \\ (iii) \quad 9801523 \\ \\\text {Sol. We know that a natural number is divisible by 4, if the number } \\ \text { formed by its digits in tens and units places is divisible by 4.} \\ \\\text {(i) Given number } =786532 \\ \text {The last two digits is 32, which is divisible by 4} \\ \therefore \quad 786532 \text { is divisible by 4.} \\ \\\text {(ii) Given number } =1020531 \\ \text {The last two digits is 31, which is not divisible by 4} \\ \therefore \quad 1020531 \text { is not divisible by 4.} \\ \\\text {(iii) Given number } =9801523 \\ \text {The last two digits is 23, which is not divisible by 4} \\ \therefore \quad 1020531 \text { is not divisible by 4.} \\ \\\text {Q5. Test the divisibility of the following numbers by 8 : } \\ (i) \quad 8364 \\ (ii) \quad 7314 \\ (iii) \quad 36712 \\ \\\text {Sol. We know that a natural number is divisible by 8, if the number } \\ \text { formed by its digits in hundreds, tens and units places is divisible by 8.} \\ \\ \text {(i) Given number } =8364 \\ \text {The number formed by hundreds, tens and units digits is 364, which is not divisible by 8} \\ \therefore \quad 8364 \text { is not divisible by 8.} \\ \\\text {(ii) Given number } =7314 \\ \text {The number formed by hundreds, tens and units digits is 314, which is not divisible by 8} \\ \therefore \quad 7314 \text { is not divisible by 8.} \\ \\\text {(iii) Given number } =36712 \\ \text {The number formed by hundreds, tens and units digits is 712, which is divisible by 8} \\ \therefore \quad 36712 \text { is divisible by 8.} \\ \\\text {Q6. Test the divisibility of the following numbers by 9 :} \\ (i) \quad 187245 \\ (ii) \quad 3478 \\ (iii) \quad 547218 \\ \\\text {Sol. We know that a natural number is divisible by 9, } \\ \text {if the sum of its digits is divisible by 9.} \\\text {(i) Sum of the digit of 187245 } = 1+8+7+2+4+5 = 27 \\ \text {Since, 27 is divisible by 9. Therefore, 187245 is divisible by 9.} \\ \\\text {(ii) Sum of the digit of 3478 } = 3+4+7+8 = 22 \\ \text {Since, 22 is not divisible by 9. Therefore, 3478 is not divisible by 9.} \\ \\\text {(iii) Sum of the digit of 547218 } = 5+4+7+2+1+8 = 27 \\ \text {Since, 27 is divisible by 9. Therefore, 547218 is divisible by 9.} \\ \\ \end{array}