Page 73 - Start Up Mathematics_6

8. Here are two different factor trees for 60. Write the missing numbers.

(a)
60

6 10

2 ? 5 ?

(b)
60

30 ?
10 ?

? ?

9. HCF of co-prime numbers 4 and 15 was found as follows by factorisation:

4 = 2 × 2 and 15 = 3 × 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?

10. 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.
11. Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Exemplar Problems

1. The number of distinct prime factors of the smallest 5-digit number is:
(a) 2 (b) 4 (c) 6 (d) 8
2. The number 7254*98 is divisible by 22, the digit at * is:

(a) 1 (b) 2 (c) 6 (d) 0
3. A number is divisible by 5 and 6. It may not be divisible by:

(a) 10 (b) 15 (c) 30 (d) 60
4. If LCM of two numbers is 180, then which of the following is not the HCF of the numbers?
(a) 45 (b) 60 (c) 75 (d) 90
5. If a number divides three numbers exactly, it must divide their sum exactly. (True/False)

6. If a number with three or more digits is divisble by 6, then the number formed by its last two
digits (i.e., ones and tens) is also divisible by 6. (True/False)
7. LCM of two or more numbers is divisible by their HCF. (True/False)
8. A merchant has 120 L of oil of one kind, 180 L of another kind and 240 L of a third kind. He
wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be
the greatest capacity of such a tin?

9. Three brands A, B and C of biscuits are available in packets of 12, 15 and 21 biscuits
respectively. If a shopkeeper wants to buy an equal number of biscuits, of each brand, what
is the minimum number of packets of each brand, he should buy?

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