Given symbols as
+ for A, - for B, × for C and \(\div \) for D
Given pattern
4 B 3 C  5 A 3 0 D 2
\(\Rightarrow\) 4 - (3 × 5) + (30 + 2)
\(\Rightarrow\) 4 - 15 + 15
= 4

i) 1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14
3 + 4 + 5 + 6 = 18
4 + 5 + 6 + 7 = 22
ii) 1 + 3 + 5 + 7 = 16
3 + 5 + 7 + 9 = 24
5 + 7 + 9 + 11 = 32
7 + 9 + 11 + 13 = 40
iii) AB, DEF, HIJK, M N O PQ, STUVWX
iv) 20, 19, 17,14, 10, 5

Given numbers are 188 and 230
Euclid's game:
HCF of 188 and 230 \(\Rightarrow\) (188, 230)
\(\Rightarrow\) (188, 230 - 188)
\(\Rightarrow\) (188,42) = 188 - 42 = 146
\(\Rightarrow\) (146, 42) = 146 - 42 = 104
\(\Rightarrow\)(104, 42) = 104 - 42 = 62
\(\Rightarrow\) (62, 42) = 62 - 42 = 20
\(\Rightarrow\) (20, 42) = 42 - 20 = 22
\(\Rightarrow\) (22, 20) = (22 - 20) = 2
\(\Rightarrow\) (2, 20) = 20 - 2 = 18
\(\Rightarrow\)(18, 2) = 18 - 2 = 16
\(\Rightarrow\)(16, 2) = 16 - 2 = 14 
\(\Rightarrow\)(14, 2)= 14 - 2 = 12
\(\Rightarrow\)(12, 2) = 12 - 2 = 10
\(\Rightarrow\)(10, 2) = 10 - 2 = 8
\(\Rightarrow\)(8, 2) \(\Rightarrow\) 8 - 2 = 6
\(\Rightarrow\) (6, 2) \(\Rightarrow\)6 - 2 = 4
\(\Rightarrow\) (4, 2) \(\Rightarrow\) 4 - 2 = 2
\(\Rightarrow\) (2, 2) 
\(\therefore\) HCF of 188 and 430 is 2.

i) Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Composite numbers = 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 22, 24, 25, 26, 27, 28, 30
ii) Odd numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31
Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28
iii) Multiplies of 6 = 6, 12, 18, 24, 30,
Multiplies of 4 = 4, 8, 12, 16, 20, 24, 28
Common multiples = 12, 24
LCM = 12
iv) Monday falls on = 7, 14, 21, 28

Now the HCF of 16, 28
16 = 2 \(\times\) 2 \(\times\)2 \(\times\) 2
28 = 2 \(\times\)2 \(\times\) 7
HCF of (16, 28) = 2 \(\times\)2 = 4
Now the HCF of (16 , 28 -16)
16 = 2 \(\times\) 2 \(\times\)2 \(\times\) 2
12 = 2 \(\times\) 2 \(\times\) 3
HCF of (16, 12) = 2 \(\times\) 2 = 4
Therefore HCF of (16, 28) = HCF of (16, 28 - 16).
Hence, HCF of two numbers a and b, a > b, is same as the HCF of a and a – b.

A - Anu
B - Bakiya
C- Chandru
D - Divya
E - Elakiya
F - Farook
G - Ganesh
H - Hema
I - Irin
J - James
K - Kala
L - Lalli
M - Maha
N - Nandhini
O - Ophiliya
P - Prabha
Q - Qasim
R - Raja
S - Srija
T - Teju
U - Uma
V - vikki
W - William
X - Xavier
Y - Yash
Z - Zamira

Given numbers are 48 and 28
HCF of 48 and 28
\(\Rightarrow\) (48, 48 - 28)
48 \(\rightarrow\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 3
20 \(\rightarrow\) 2 \(\times\) 2 \(\times\) 5
HCF = 2 \(\times\) 2 = 4
Also find : HCF of 48 and 4
48 \(\rightarrow\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 3
4 \(\rightarrow\) 2 \(\times\) 2
HCF=2 \(\times\) 2 = 4
Difference = 4 - 4 = 0 [same HCF]

(i) 50, 51, 53, 56, 60 
The next three numbers will be 65, 71, 78 .......
(ii) 77, 69, 61, 53 
The next three numbers will be 45, 37, 29 .....
(iii) 10, 20, 40, 80
The next three numbers will be 160, 320, 640 .....
(iv) \(\cfrac { 21 }{ 33 } ,\cfrac { 321 }{ 444 } ,\cfrac { 4321 }{ 5555 } \)
The next three numbers will be \(\cfrac { 54321 }{ 66666 } ,\cfrac { 654321 }{ 777777 } ,\cfrac { 7654321 }{ 888888 } ,\)

(i) 1 \(\times\) 1 = 1
11 \(\times\) 11 = 121
111 \(\times\) 111 = 12321
1111 \(\times\) 1111 = 1234321
11111 \(\times\) 11111 = 123454321
(ii)

604 is common fer all postal Index numbers. Compare the remaining 3 digits are
604303, 604470, 604505, 604506 [2 times]
604509, 604510, 604515, 604516 [4 times]
604520, 604560 [2 times]
604 is common for all postal index numbers. Compare the remaining 3 digits 303, 470, 505, 506 (two) 509, 510, 515, 516 (four), 520, 560 (two).
604303; 604470; 604505; 604506; 604506; 604509; 604510; 604515; 604516; 604516; 604516; 604516; 604520; 604560; 604560

Euclid's game
(28, 35, 41)
\(\Rightarrow\) (28, (35 - 28), (42 - 28))
\(\Rightarrow\) (28, 7, 14)
\(\Rightarrow\) (28 -7), 7, 14 - 7)
\(\Rightarrow\) (21, 7, 7) \(\Rightarrow\)((21 -7), 7, 7)
\(\Rightarrow\) (14, 7, 7) 
\(\Rightarrow\) (14 - 7, 7, 7)
\(\Rightarrow\)(7, 7, 7)
\(\therefore\) HCF of (28, 35, 42) is 7