Which of the following numbers is a divisor of \((49^{15} - 1) \)?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
View all SSC CGL Papers >
  1. 46
  2. 14
  3. 8
  4. 50

Answer (Detailed Solution Below)

Option 3 : 8
ssc-cgl-crash
Free
PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
1.9 Lakh Users
25 Questions 50 Marks 20 Mins

Detailed Solution

Download Solution PDF

Given:

\((49^{15} - 1) \)

Concept used:

an​​​​​​ - bn is divisible by (a + b) when n is an even positive integer.

Here, a & b should be prime number.

Calculation:

\((49^{15} - 1) \)

⇒ \(({(7^2)}^{15} - 1) \)

⇒ \((7^{30} - 1) \)

Here, 30 is a positive integer.

​According to the concept,

\((7^{30} - 1) \) is divisible by (7 + 1) i.e., 8.

∴ 8 is a divisor of \((49^{15} - 1) \).

Latest SSC CGL Updates

Last updated on Jun 9, 2025

-> The SSC CGL Notification 2025 will be released on 9th June 2025 at ssc.gov.in.

-> The SSC CGL application 2025 submission will be open from 9th June to 4th July 2025. 

-> The SSC CGL Tier 1 Exam 2025 Dates have been revised. The SSC CGL Exam will be conducted from 13 August to 30 August, 2025.

-> Candidates can refer to the SSC CGL syllabus for a better understanding of the exam structure and pattern.

-> The SSC CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> Candidates should also use the SSC CGL previous year papers for a good revision. 

Get Free Access Now
Hot Links: teen patti 100 bonus teen patti download teen patti refer earn