2) Write the divisibility rule by 11 with one example.
7) What is the capacity of the largest vessel which can empty the oil from
containing 32 litres, 24 litres and 48 litres respectively, an exact number
3) Fill the table with correct answer.
Any tvo consecutive
numbers
Any two
consecutive
even numbers
od
Two numbers with
numbers or relativ
Divisibility by 2,
Divisibility by 3
Divisibility by 4
(iv) Divisibility of 11
places.
If two numbers are di
divisible by th
The highest
highest of the
The least co
lowest of th
If one of the two
will be their LCM
Relationship
bet
LCM X HCF =
H.CF of
4) Find HCF of 70, 105, and 175 by prime factorisation method
5) Find HCF of 18, 54, 81 by continued division method.
6) Find LCM of 4. 12. 24 by two methods.
8) HCF, LCM of two number are 9 and 54 respectively. If one of those
18, find the other number
ties
matics
Answers
(2)
Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.
So, for instance, 2728 has alternating sum of digits 2 – 7 + 2 – 8 = -11. Since -11 is divisible by 11, so is 2728.
Similarly, for 31415, the alternating sum of digits is 3 – 1 + 4 – 1 + 5 = 10. This is not divisible by 11, so neither is 31415.
(3)
it would be the LCM of 32,24,48.
32=2×2×2×2×2
24=2×2×2×3
48=2×2×2×2×3
so LCM=2×2×2×2×3×2×3×2 =576
32×18=576
24×24=576
48×12=576
So In single Handed approach.
The largest vessel whose volume is 576 L can Empty 32 L vessel 18 times. 24 L vessel 24 times. and 48 L vessel 12 Times.
(4)
Factors of 70 = 2 x 5 x 7
Factors of 105 = 3 x 5 x 7
Factors of 175 = 5 x 5 x 7
H.C.F. = 5 x 7 = 35
(5)
The first number completely divides the second number so now we will divide the third number with the first number.
On getting the remainder we again divide the dividend with the quotient and it completely divides it. So this quotient is your answer.
You answer is 9.
18 l---l 3
54
- 54
- - - - -
00
(6)
2 is the LCM of 4,12,16 and 24.
(8)
Lcm×Hcf = a×b
54×9 = 18×b
54×9/18 =b
b=27