What is the HCF of 3²9} - 9 and 3³8} - 9 ?

Correct Answer is : 311−93¹1} - 9311−9

Correct Answer is : 311−93¹1} - 9311−9

Test Index

UPSC CDS 1 2023 Math Paper

Question : 24 of 100

Marks: +1, -0

3^{29} - 9

3^{38} - 9

Solution:

Concept:

The HCF of

a^m - 1

and

a^n - 1

a^{\text{HCF}(m,n)} - 1

Explanation:

First, factor out the common

3^2

from both numbers because

9 = 3^2

3^{29} - 9 = 3^2(3^{27} - 1)

and

3^{38} - 9 = 3^2(3^{36} - 1)

Now find the HCF of

3^{27} - 1

and

3^{36} - 1

using the concept above.

The HCF of

(3^{27} - 1)

and

(3^{36} - 1)

3^{\text{HCF}(27,36)} - 1 = 3^9 - 1

Since

3^2

is also a common factor, multiply it to get the final HCF:

HCF

= 3^2 \times (3^9 - 1) = 3^{11} - 9

Answer:

3^{11} - 9

(Option D).

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