shriti wrote:If n is a positive integer and n squared is divisible by 72, then the largest possible integer that must divide n is
a. 6
b. 12
c. 24
d. 36
e. 48
The prime factor of 72 are -> 2, 2, 2, 3, 3
n² is divisible by 72 HENCE 2, 2, 2, 3, 3, ...? (2², 2, 3²)are prime factors of n² ("...?" because there could be more prime factors)
Because n² must have at least (2², 2, 3²) in its prime factors, and n² = n * n, we can distribute this factors to determine the prime factors of n:
n²
=
n -> 2 * 3 * 2
*
n -> 2 * 3 *
2 We must fill this space with "2" to obtain two equal values of n
[spoiler]So the largest number that must divide n is 2 * 3 * 2, which is 12 (1, 2, 3, and 6 could divide n but 12 is the largest one)
Correct Answer is ...B...[/spoiler]
