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N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer?
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N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural numbe...
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N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural numbe...
Introduction:
The given expression is N^2-1, and we have to determine if it is divisible by 8 or not. We need to find out the nature of N that will make N^2-1 divisible by 8.
Solution:
To determine the divisibility of N^2-1 by 8, we need to use the concept of remainders. We know that if a number is divisible by 8, its remainder when divided by 8 will be zero.
Step 1: Express N^2-1 in terms of factors.
N^2-1 can be expressed as (N+1)(N-1).
Step 2: Determine the nature of N that will make (N+1)(N-1) divisible by 8.
For (N+1)(N-1) to be divisible by 8, both (N+1) and (N-1) must be even.
If N is odd, then both (N+1) and (N-1) will be even, and hence (N+1)(N-1) will be divisible by 8.
If N is even, then either (N+1) or (N-1) will be odd, and hence (N+1)(N-1) will not be divisible by 8.
Conclusion:
Hence, we can conclude that N^2-1 is divisible by 8 if N is an odd integer.
The given expression is N^2-1, and we have to determine if it is divisible by 8 or not. We need to find out the nature of N that will make N^2-1 divisible by 8.
Solution:
To determine the divisibility of N^2-1 by 8, we need to use the concept of remainders. We know that if a number is divisible by 8, its remainder when divided by 8 will be zero.
Step 1: Express N^2-1 in terms of factors.
N^2-1 can be expressed as (N+1)(N-1).
Step 2: Determine the nature of N that will make (N+1)(N-1) divisible by 8.
For (N+1)(N-1) to be divisible by 8, both (N+1) and (N-1) must be even.
If N is odd, then both (N+1) and (N-1) will be even, and hence (N+1)(N-1) will be divisible by 8.
If N is even, then either (N+1) or (N-1) will be odd, and hence (N+1)(N-1) will not be divisible by 8.
Conclusion:
Hence, we can conclude that N^2-1 is divisible by 8 if N is an odd integer.
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N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer?
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N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer?.
N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for N^2-1 is divisible by 8 if n is an (a) an integer (b) an natural number (c) an odd integer (d) an even integer?.
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