Question

The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1? (1) The greatest common factor of m and p is 2. (2) The least common multiple of m and p is 30.

Answer 1

Yes. r>1

Explanation:

First we write the information we have.

2<m<p and m and p are integers

(1) The greatest common factor is 2. So we can say

2 is a factor of m and p.

(3) The minimum common multiple of m and p is 30.

So we can say that 30 can be divided by m and also by p.

So we will write all the dividers of 30.

1 ; 2 ; 3 ; 5; 6; 10; 15; 30

Of all this integers, the only ones that can be divided by 2 are:

2. 6 and 10.

Also, we know that m is not a factor of p. So we know that it cant be 2. because both 6 and 10 can be divided by 2.

That means m = 6 and p = 10.

So if r is the remainder of p divided by m. When we divided 10 by 6, we have a remainder of 4. r=4. Then r>1.