I have a patio which is 3m wide. The roof of this consists of sheets of plastic which are 900mm wide. I have used as few sheets as possible and made all overlaps the same width. What is the width, in millimetres, of this overlap?
A. 100
B. 150
C. 200
D. 250
E. 300
To find the width of the overlap, we need to find the common factor between the width of the patio (3m = 3000mm) and the width of the plastic sheets (900mm).
Step 1: Find the greatest common divisor (GCD) between 3000 and 900.
The prime factorization of 3000:
3000 = 2 * 2 * 2 * 3 * 5 * 5 * 5
The prime factorization of 900:
900 = 2 * 2 * 3 * 3 * 5 * 5
Step 2: Determine the common factors between the two numbers by multiplying the common prime factors.
Common factors: 2 * 2 * 3 * 5 * 5 = 300
The width of the overlap is 300mm, so the answer is E. 300.