2 math questions?

Question

QUESTION #1

Betty is covering a wall with equal-sized tiles that can't be cut into smaller pieces. The area he wishes to cover is 66 in. high by 72 in. wide. What is the largest square tile that Betty can use?

QUESTION #2

A photography club is practicing developing techniques. One set of negatives contains 32 negatives and another contains 48 negatives. Each set can be divided equally among the members present. List all the possible numbers of members present. What is the greatest possible number?

Thank you :]]

Answer 1

1) 6 inch squares.

2) 1, 2, 4, 8, 16

Answer 2

Basically, these are Greatest Common Multiple (GCM) questions, so first find the prime factors of each number...

#1)
66 = 2 x 3 x 11
72 = 2 x 2 x 2 x 3 x 3

GCM is 2 x 3 = 6

or a square six inches on each side


#2)
32 = 2 x 2 x 2 x 2 x 2
48 = 2 x 2 x 2 x 2 x 3

This one a little different as the GCM is the largest number possible, but the problem also wants you to list all possible sets.

GCM is 2 x 2 x 2 x 2 = 16,
but the following also work

2
2 x 2 = 4
2 x 2 x 2 = 8

But don't forget that 1 is also a factor for everything, so it should be included also.

so the answer is 1, 2, 4, 8, and 16

Answer 3

66 in x 72 in will have largest square tile 6 in x 6 in.

least 2, 4, 8, 16 greatest.

Answer 4

question #1
Might be 2 becuase 2 can be 66 or 72 try that

Answer 5

1

Answer 6

question one is 6 x 6.