Question

16. Find the greatest number which divides 82 and 132 leaving 1 and 6. respectively
remainders.​

Answer 1

Answer:

9

Step-by-step explanation:

82-1= 81

132-6=126

81)126(1

-81

45)81(1

-45

36)45(1

-36

9)36(4

-36

0

Answer 2

$\mathfrak{Question:}$

Find the greatest number which divides 82 and 132 leaving 1 and 6 respectively as remainder.

$\mathfrak{Solution:}$

• To find the greatest number, we've to find the H.C.F of ( 82 - 1 ) and     ( 132 - 6 ).

82 - 1 = 81

132 - 6 = 126

Now,

81 = 3 × 3 × 3 × 3

126 = 3 × 3 × 2 × 7

∴ H.C.F = 3 × 3

= 9

So, 9 is the greatest no. that divides 81 and 132.