raja11010 wrote:Could some one post me the explanation for this (yes/no type) question..
If 80 is a factor of r,is 15 a factor of r?
regards
Raja.
When it comes to factors/divisors, I find it useful to relate information to the prime factorization of a number.
For example, if we know that
5 is a divisor of 70, we can say that 5 is "hiding" in the prime factorization of 70.
Prime factorization of 70: 70 = (2)(
5)(7)
Similarly, if
6 is a divisor of 210, we can say that 6 is "hiding" in the prime factorization of 120.
Prime factorization of 120: 120 =
(2)(3)(5)(7) [here, the 6 is in the form (2)(3)]
If we are told that
15 is a factor of M, then we know that 15 will be "hiding" in the prime factorization of M. In other words,
(3)(5) will be "hiding" in the prime factorization of M
So, we know that M =
(3)(5)(?)(?)(?)(?) where the ?'s represent other possible prime numbers in the prime factorization of M
To answer your question, if
80 is a factor of r then we know that
80 is "hiding" in the prime factorization of r.
Since
80 is also known as
(2)(2)(2)(2)(5), we know that prime factorization of r looks like this:
r =
(2)(2)(2)(2)(5)(?)(?)(?)(?) where the ?'s represent other possible prime numbers in the prime factorization of r
For 15 to be a factor of r, it must be true that 15 is hiding in the PF of r. In other words (3)(5) must be hiding in the PF of r.
At the moment, all we know is that r =(2)(2)(2)(2)(5)(?)(?)(?)(?)
So, we know for certain that a (5) is hiding in the PF of r, but we can't say for certain that a (3) is hiding in the PF of r.
As such, we can't determine with any certainty whether or not 15 is a factor of r.
