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6th Class Mathematics Playing with Numbers

Playing with Numbers [Download Complete Solution]

1) Write all the factors of the following numbers (a) 24 (b) 15 (c) 21 (d) 27 (e) 12 (f) 20 (g) 18 (h) 23 (i) 36
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2) Write first five multiples of (a) 5 (b) 8 (c) 9
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3) Match the items in column 1 with the items in column 2.
Column I Column II (i) 35 (a) Multiple of 8 (ii) 15 (b) Multiple of 7 (iii) 16 (c) Multiple of 70 (iv) 20 (d) Factor of 30 (v) 25 (e) Factor of 50 (f) Factor of 20

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4) Find all the multiples of 9 upto 100.
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5) What is the sum of any two (a) odd numbers? (b) even numbers? TIPS We know that a number is called an even number, if it is completely divided by 2 (i.e. remainder = 0). Otherwise, it is an odd number.
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6) State whether the following statements are true or false. (a) The sum of three odd numbers is even. (b) The sum of two odd numbers and one even number is even. (c) The product of three odd numbers is odd. (d) If an even number is divided by 2, the quotient is always odd. (e) All prime numbers are odd. (f) Prime numbers do not have any factor. (g) Sum of two prime numbers is always even. (h) 2 is the only even prime number. (i) All even numbers are composite numbers. (j) The product of two even numbers is always even.
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7) The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.
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8) Write down separately the prime and composite numbers less than 20.
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9) What is the greatest prime number between 1 and 10?
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10) Express the following as the sum of two odd primes. (a) 44 (b) 36 (c) 24 (d) 18
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11) Give three pairs of prime numbers whose difference is 2. [Remark Two prime numbers whose difference is 2 are called twin primes].
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12) Which of the following numbers are prime? (a) 23 (b) 51 (c) 37 (d) 26 TIPS To check these given numbers, firstly we divide each number individually by the prime numbers, less than each. If any number is not completely divided by prime numbers, it would be a prime number.
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13) Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
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14) Express each of the following numbers as the sum of three odd primes. (a) 21 (b) 31 (c) 53 (d) 61
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15) Write five pairs of prime numbers less than 20, whose sum is divisible by 5. (Hint 3 + 7 = 10)
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16) Fill in the blanks. (a) A number which has only two factors is called a ________ . (b) A number which has more than two factors is called a ________ . (c) 1 is neither ________ nor ________. (d) The smallest prime number is ________. (e) The smallest composite number is ________. (f) The smallest even number is ________.
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17) Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no)?
Number Divisible by 2 3 4 5 6 8 9 10 11 (i) 128 Yes No Yes No No Yes No No No (ii) 990 (iii) 1586 (iv) 275 (v) 6686 (vi) 639210 (vii) 429714 (viii) 2856 (ix) 3060 (x) 406839

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18) Using divisibility tests, determine which of the following numbers are divisible by 4 and 8? (a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150
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19) Using divisibility tests, determine which of the following numbers are divisible by 6? (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852
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20) Using divisibility tests, determine which of the following numbers are divisible by 6? (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852
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21) Using divisibility tests, determine which of the following numbers are divisible by II? (a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153 TIPS Firstly, find the difference between the sum of the digits at odd places ' (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11, otherwise not.
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22) Write the smallest digit and the greatest digit in the blank space of each of the following numbers, so that the number formed is divisible by 3: (a) ____ 6724 (b) 4765 ____ 2 TIPS Firstly, find the sum of digits of given number, then subtract it from those multiples of 3, which are greater than this sum to get smallest and greatest digit.
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23) Write a digit in the blank space of each of the following numbers, so that the number formed is divisible by 11. (a) 92 ____ 389 (b) 8 ____ 9484 TIPS Firstly, assume the blank space digit as \[x\], then find the sum of odd places and even places digits (from the right) separately. Now, take difference of sum of odd places digits and sum of even places digits equal to 0 or 11 and simplify to get the value of \[x\].
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24) Find the common factors of (a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120
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25) Find the common factors of (a) 4, 8 and 12 (b) 5, 15 and 25
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26) Find first three common multiples of (a) 6 and 8 (b) 12 and 18
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27) Write all the numbers less than 100 which are common multiples of 3 and 4.
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28) Which of the following numbers are co-prime? (a) 18 and 35 (b) 15 and 37 (c) 30 and 415 (d) 17 and 68 (e) 216 and 215 (f) 81 and 16 TIPS Firstly, write the factors of given numbers. If two numbers have only 1 as common factor, then they are called co-prime numbers otherwise not.
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29) A number is divisible by both 5 and 12. By which other number will that number be always divisible?
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30) A number is divisible by 12. By what other numbers will that number be divisible?
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31) Which of the following statements are true? (a) If a number is divisible by 3, it must be divisible by 9. (b) If a number is divisible by 9, it must be divisible by 3. (c) A number is divisible by 18, if it is divisible by both 3 and 6. (d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. (e) If two numbers are co-prime, atleast one of them must be prime. (f) All numbers which are divisible by 4 must also be divisible by 8. (g) All numbers which are divisible by 8 must also be divisible by 4. (h) If a number exactly divides two numbers separately, it must exactly divide their sum. (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
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32) Here are two different factor trees for 60. Write the missing numbers. (a) (b)
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33) Which factors are not included in the prime factorization of a composite number?
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34) Write the greatest 4-digit number and express it in terms of its prime factors.
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35) Write the smallest 5-digit number and express it in the form of its prime factors.
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36) Find all the prime factors of 1729 and arrange them in ascending order. Now, state the relation, if any, between two consecutive prime factors.
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37) The product of three consecutive numbers is, always divisible by 6. Verify this statement with the help of some examples.
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38) The sum of two consecutive odd numbers is divisible by 4. Verify this statements with the help of some examples.
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39) In which of the following expressions, prime factorisation has been done? (a) \[24=2\times 3\times 4\] (b) \[56=7\times 2\times 2\times 2\] (c) \[70=2\times 5\times 7\] (d) \[54=2\times 3\times 9\]
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40) Determine, if 25110 is divisible by 45. [Hint 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9]. TIPS If a number is divisible by two co-prime numbers, then it is divisible by their product also.
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41) 18 is divisible by both 2 and 3. It is also divisible by \[2\times 3=6.\] Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by \[4\times 6=24?\] If not, give an example to justify your answer.
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42) I am the smallest number, having four different prime factors. Can you find me?
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43) Find the HCF of the following numbers. (a) 18, 48 (b) 30, 42 (c) 18, 60 (d) 27, 63 (e) 36, 84 (i) 34, 102 (g) 70, 105,175 (h) 91, 112, 49 (i) 18, 54, 81 (j) 12, 45, 75
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44) What is the HCF of two consecutive (a) numbers? (b) even numbers? (c) odd numbers?
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45) HCF of co-prime numbers 4 and 15 was found as follows by factorisation. \[4=2\times 2\] and \[15=3\times 5,\] since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?
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46) Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight, which can measure the weight of the fertiliser exact number of times.
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47) Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm, respectively. What is the minimum distance each should cover, so that all can cover the distance in complete steps?
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48) The length, breadth and height of a room are 825 cm, 675 cm and 450 cm, respectively. Find the longest tape, which can measure the three dimensions of the room exactly.
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49) Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.
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50) Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
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51) The traffic lights at three different road crossings change after every 48 seconds 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?
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52) Three tankers contain 403 Litres 434 Litres and 465 Litres of diesel, respectively. Find the maximum capacity of a container, that can measure the diesel of the three containers exact number of times.
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53) Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.
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54) Find the smallest 4-digit number which is divisible ay 18, 24 and 32.
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55) Find the LCM of the following numbers (a) 9 and 4 (b) 12 and 5 (c) 6 and 5 (d) 15 and 4 Observe a common property in the obtained LCM. Is LCM the product of two numbers in each case?
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56) Find the LCM of the following numbers in which one number is the factor of the other. (a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9,45 What do you observe in the results obtained?
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