Discussion
Which one of the following numbers is the greatest positive integer x such that 3x is a factor of 275?
*This question is included in Nova Math - Problem Set F: Number Theory, question #15
| (A) | 5 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 04/02/2013 21:40
Could you break this one down?
Posted: 04/04/2013 05:14
Hi Tom,
27 = 3^3, so we replaced 27 with 3^3 and then multiplied the exponents (3 and 5) to get 3^15.
Since we have written 27^5 as product of only 3's (27 = 3^15), we cannot squeeze out any more 3's from 27^5. Hence, x = 15 is the largest possible integer.
Nova Press
27 = 3^3, so we replaced 27 with 3^3 and then multiplied the exponents (3 and 5) to get 3^15.
Since we have written 27^5 as product of only 3's (27 = 3^15), we cannot squeeze out any more 3's from 27^5. Hence, x = 15 is the largest possible integer.
Nova Press