Question

22) Find the greatest number which divides 82 and 132 leaving remainders 1 and 6 respectively.

Answer 1

Answer:

9 is the greatest no. which divides 82 and 132 leaving 1 and 6 respectively as remainder.

In order 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

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

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

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.

Step-by-step explanation: