What is length of an integer XXXXX ?

frank1 wrote:What is length of an integer XXXXX ?

Length of an integer = total # of Prime factors in its prime factiorization

ramannjit wrote:
Length of an integer = total # of Prime factors in its prime factiorization

599 is a prime number so as per your definition of Length of an integer is
599 has only 2 prime factors 1 and 599 so i think answer must be 2.

goyalsau wrote:

ramannjit wrote:
Length of an integer = total # of Prime factors in its prime factiorization

599 is a prime number so as per your definition of Length of an integer is
599 has only 2 prime factors 1 and 599 so i think answer must be 2.

I thought that way but the answer is "9"

IF you have the official solution
then please post it over here, it will help a lot in understanding
that why the answer is 9.

ramannjit wrote:What is the maximum possible length of an integer less than 600?

Help me get to OA with steps.


OA 9

The length of an integer is the number of prime factors you get when the number is prime-factorized:

The length of 35 is 2 because 35 = 5*7 (2 prime factors = length of 2)
The length of 8 is 3 because 8 = 2*2*2 (3 prime factors = length of 3)

You do not need to memorize this definition. If the length of an integer is discussed on the GMAT, the definition will be provided.

To get the maximum possible length, we need to use only the smallest prime number, which is 2.

2*2*2*2*2*2*2*2*2 = 512. 9 prime factors gives us a length of 9. This is the maximum possible length of an integer less than 600. If we add another 2, we'll get a product that is too big: 2^10 = 1024.

GMATGuruNY wrote:

ramannjit wrote:What is the maximum possible length of an integer less than 600?

Help me get to OA with steps.


OA 9

The length of an integer is the number of prime factors you get when the number is prime-factorized:

The length of 35 is 2 because 35 = 5*7 (2 prime factors = length of 2)
The length of 8 is 3 because 8 = 2*2*2 (3 prime factors = length of 3)

You do not need to memorize this definition. If the length of an integer is discussed on the GMAT, the definition will be provided.

To get the maximum possible length, we need to use only the smallest prime number, which is 2.

2*2*2*2*2*2*2*2*2 = 512. 9 prime factors gives us a length of 9. This is the maximum possible length of an integer less than 600. If we add another 2, we'll get a product that is too big: 2^10 = 1024.

Thanks for the explanation. I have a small concern:

Can we infer that the maximum possible length of an integer less than 1023 is 9 and that of integer less than 2047 is 10?

shovan85 wrote:

GMATGuruNY wrote:

ramannjit wrote:What is the maximum possible length of an integer less than 600?

Help me get to OA with steps.


OA 9

The length of an integer is the number of prime factors you get when the number is prime-factorized:

The length of 35 is 2 because 35 = 5*7 (2 prime factors = length of 2)
The length of 8 is 3 because 8 = 2*2*2 (3 prime factors = length of 3)

You do not need to memorize this definition. If the length of an integer is discussed on the GMAT, the definition will be provided.

To get the maximum possible length, we need to use only the smallest prime number, which is 2.

2*2*2*2*2*2*2*2*2 = 512. 9 prime factors gives us a length of 9. This is the maximum possible length of an integer less than 600. If we add another 2, we'll get a product that is too big: 2^10 = 1024.

Thanks for the explanation. I have a small concern:

Can we infer that the maximum possible length of an integer less than 1023 is 9 and that of integer less than 2047 is 10?

Yes, your inferences are correct.

GMATGuruNY wrote:

ramannjit wrote:What is the maximum possible length of an integer less than 600?

Help me get to OA with steps.


OA 9

The length of an integer is the number of prime factors you get when the number is prime-factorized:

The length of 35 is 2 because 35 = 5*7 (2 prime factors = length of 2)
The length of 8 is 3 because 8 = 2*2*2 (3 prime factors = length of 3)

You do not need to memorize this definition. If the length of an integer is discussed on the GMAT, the definition will be provided.

To get the maximum possible length, we need to use only the smallest prime number, which is 2.

2*2*2*2*2*2*2*2*2 = 512. 9 prime factors gives us a length of 9. This is the maximum possible length of an integer less than 600. If we add another 2, we'll get a product that is too big: 2^10 = 1024.

Thanks Hunt for explaination. So it is the only way for solving this type of question "To get the maximum possible length, we need to use only the smallest prime number, which is 2."
goyalsau: Sorry, seen your post late. Explaination to this was like Hunt has given but a very long drawn. Crux of the answer is quoted and bolded above.

Thanks for help:)

Dear raman

if guru would not have given the explanation i was not able to figure it out.
But the problem with these type of questions is that, there you have to remember some formulas.. and that is the worst part because logic can remain with us for ever but my memory is very bad when it comes to formulas..

Just to add in...
I suppose its not abt the formulas... eventually its logic..
if u need to find the maximum length, then u need to choose the smallest prime, as that prime will successively divide a big number many more times than a bigger prime...

for this particular question 2^9 is the closest...

but there could also be a combination of 2 and 3 which could give u a length more than just the power of 2's...

All iam saying is... that logic should be clear..

goyalsau wrote:Dear raman

if guru would not have given the explanation i was not able to figure it out.
But the problem with these type of questions is that, there you have to remember some formulas.. and that is the worst part because logic can remain with us for ever but my memory is very bad when it comes to formulas..

Yes Dear, true, it is with most people! but once you go through the discussion, your chances of remembering the breakdown increases to many folds, that you did something like that. A big hint for this question is as Guru mentioned "You do not need to memorize this definition. If the length of an integer is discussed on the GMAT, the definition will be provided. " once you see a hint for this question on the test, you will recall this post

Thanks