My explanation is somewat different:)

Given, p = mA + r ( m is some integer)

1)

m and p have 2 as the greatest common factor, so

m = 2 * I1

p = 2 * I2

now, 2*I2 = 2*I1 + r , but it is given that , p > m , so, I2 > I1 => I2-I1 > 0

therefore, 2 (I2-I1) = r => r > 1.

2)

m and p have 30 as the LCM.

m = 2*3*5 * I1 ( but I1 can have more 2's 3's or 5's).

p = 2*3*5 * I2 ( but I2 can have more 2's 3's or 5's).

So we cant have a relation between I2 and I1. hence we cant prove that r > 1.

Accountant wrote:

Integers m and p are such that 2<m<p and m in NOT a factor of p. If r is the remainder when p is divided by m, is r>1?

1. Greatest common factor of m and p is 2.

2. Least common multiple of m and p is 30.

Please explain your answers.