if A=2n+13, B=n+7 ,where n is a natural number, then find the HCF of A and B
Answers
Solution :-
A = 2n + 13
B = n + 7
1) If the value of n = 1, then
A = (2*1) + 13
= 2 + 13
= 15
B = 1 + 7
= 8
Now, A = 15 and B = 8
HCF of 15 and 8 is 1.
2) If the value of n =2
A = (2*2) + 13
= 4 + 13
= 17
B = 2 + 7
= 9
A = 17 and B = 9
HCF of 17 and 9 is 1.
3) If the value of n 3
A = (2*3) + 13
= 6 + 13
= 19
B = 3 + 7
= 10
A = 19 and B = 10
HCF of 19 and 10 is 1
4) If the value of n = 4
A = (2*4) + 13
= 8 +13
= 21
B = 4 + 7
= 11
A = 21 and B = 11
HCF of 21 and 11 is 1
5) If the value of n = 5
A = (2*5) + 13
= 10 + 13
= 23
B = 5 + 7
= 12
A = 23 and B = 12
HCF of 23 and 12 is 1
6) If the value of n = 6
A = (2*6) + 13
= 12 + 13
= 25
B = 6 + 7
= 13
A = 25 and B = 13
HCF of 25 and 13 is 1
7) If the value of n = 7
A = (2*7) + 13
14 + 13
= 27
B = 7 + 7
= 14
A = 27 and B = 14
HCF of 27 and 14 is 1
8) If the value of n = 8
A = (2*8) + 13
16 + 13
= 29
B = 8 + 7
= 15
A = 29 and B = 15
HCF of 29 and 15 is 1
9) If the value of n = 9
A = (2*9) + 13
18 + 13
= 31
B = 9 + 7
= 16
A = 31 and B = 16
HCF of 31 and 16 is 1
10) If the value of n = 10
A = (2*10) + 13
20 + 13
= 33
B = 10 + 7
= 17
A = 33 and B = 17
HCF of 33 and 17 is 1
We have seen that whatever the value n has, the HCF of A and B (separate values they hold in each situation) is always 1. It means we can take any value of n and the HCF will be 1. Hope it will help you....