This is one of those GRE questions
column A
The greatest prime factor of 3^5
column B
The greatest prime factor of 5^3
a)column a is greater
b)column b is greater
c)the quantities are equal
d)relationship cannot be determined
A prime number is a positive integer greater than 1
which is not divisible by any number except itself
and 1.
All the factors are 3, 3^2, 3^3, 3^4 and 3^5.
3 is not divisible by any positive integer besides itself, 3, and
1 and it is greater than 1, so it IS a prime factor of 3^5
3^2, which is 9, is divisible by the positive integer 3, and 3 is
a positive integer other than 9. So it is NOT a prime factor of 3^5.
3^3, which is 27, is divisible by the positive integer 3, and 3 is
a positive integer other than 27. So it is NOT a prime factor of 3^5.
3^4, which is 81, is divisible by the positive integer 3, and 3 is
a positive integer other than 81. So it is NOT a prime factor of 3^5.
3^5, which is 243, is divisible by the positive integer 3, and 3 is
a positive integer other than 243. So it is NOT a prime factor of 3^5.
Therefore the largest prime factor of 3^5 is 3. [Can you see, from the
pattern above that 3 is the largest prime factor of even
3*1000000000 ?]
Can you also see, by the same reasoning, that the largest prime factor
of 5^3 is 5?
answer (a) says 3 is greater than 5. We know that's incorrect.
answer (b) says 5 is greater than 3. We know that's correct.
answer (c) says 3 is equal to 5. We know that's incorrect.
answer (d) say which is larger cannot be determined. We know that's
incorrect because we can determine that 5 is greater than 3.
The only correct answer is (b)
Edwin
