Class 10 Exam > Class 10 Questions > If a is a positive integer and p be a prime n...
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If a is a positive integer and p be a prime number and p divides a2, then
- a)a divides p
- b)p divides a
- c)p2 divides a
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If a is a positive integer and p be a prime number and p divides a2, t...
We have a=(p1.p2.p3.p4.p5..pn) and p is one of the numbers from (p1.p2.p3.p4.p5.pn).
It means that p also divides a.
Most Upvoted Answer
If a is a positive integer and p be a prime number and p divides a2, t...
As p divides a²,then p divides a also.
For example, if 5 divides 10², 5 divides 10 also.
So correct option is B
For example, if 5 divides 10², 5 divides 10 also.
So correct option is B
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Community Answer
If a is a positive integer and p be a prime number and p divides a2, t...
Explanation:
To prove that option 'B' is the correct answer, we need to understand the given conditions and analyze each option.
Given conditions:
- 'a' is a positive integer.
- 'p' is a prime number.
- 'p' divides 'a^2'.
Analyzing each option:
a) a divides p:
This option is not necessarily true. For example, let's take a = 2 and p = 3. Here, 3 divides 2^2 (9), but 2 does not divide 3.
b) p divides a:
This option is the correct answer. Since 'p' divides 'a^2', we can say that 'p' divides 'a' as well. This is because if 'p' does not divide 'a', it cannot divide 'a^2' either. Therefore, option 'B' is true.
c) p^2 divides a:
This option is not necessarily true. For example, let's take a = 3 and p = 2. Here, 2 divides 3^2 (9), but 2^2 (4) does not divide 3.
d) None of these:
This option is not the correct answer since we have already established that option 'B' is true.
Conclusion:
From the analysis above, we can conclude that option 'B' is the correct answer. Prime number 'p' divides the positive integer 'a' when 'p' divides 'a^2'.
To prove that option 'B' is the correct answer, we need to understand the given conditions and analyze each option.
Given conditions:
- 'a' is a positive integer.
- 'p' is a prime number.
- 'p' divides 'a^2'.
Analyzing each option:
a) a divides p:
This option is not necessarily true. For example, let's take a = 2 and p = 3. Here, 3 divides 2^2 (9), but 2 does not divide 3.
b) p divides a:
This option is the correct answer. Since 'p' divides 'a^2', we can say that 'p' divides 'a' as well. This is because if 'p' does not divide 'a', it cannot divide 'a^2' either. Therefore, option 'B' is true.
c) p^2 divides a:
This option is not necessarily true. For example, let's take a = 3 and p = 2. Here, 2 divides 3^2 (9), but 2^2 (4) does not divide 3.
d) None of these:
This option is not the correct answer since we have already established that option 'B' is true.
Conclusion:
From the analysis above, we can conclude that option 'B' is the correct answer. Prime number 'p' divides the positive integer 'a' when 'p' divides 'a^2'.
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