Question 1
p and q are
both prime numbers.
Find the values of p and q such that 
is an integer.
Question 2
One third of the
product of 68 and 108 is the same as 2p x 3q x 17r
Find p, q, and r.
Question 3
Find smallest
positive integer k for 
be a perfect cube
Solution:
Written as a
product of its prime factors, 540 = 22 x 33 x 5
(i)
Find the smallest positive integer k such that 540k is a
perfect cube.
(ii)
Give an example of a positive integer value of h
such that 
is a perfect cube
Written as a
product of its prime factors, 600 = 22 x 3 x 52
Find the
smallest positive integer k such that 
is a perfect square
Find the smallest possible whole number k if 3575k is a multiple of 260.
The numbers
of 700 and 1050, written as the products of their prime factors, are
700 = 22 x 52
x 7,
1050 = 2 x 3 x 52 x 7
Find
(i)
The smallest positive integer h for
which 700h is a multiple of 1050
(ii)
The smallest positive integer k for
which 
is a factor of
700
