Determine whether or not each number is a common factor of 144 and 240. try to use different methods, and show your work. a) 2 b) 3 c) 10 d) 48 e) 120

Step-by-step explanation:

2| 144

2|  72

2|   36

2|  18

3|  9

|  3

144=2×2×2×2×3×3

2 | 240

2 | 120

2  | 60

2  | 30

3  | 15

   |  5

240=2×2×2×2×3×5

greatest common factor=2×2×2×2×3=48

a. 2 divides both ,so common factor

b. 3 divides both ,so common factor

c. 10 does not divide 144  so not a common factor.

d.48 divides both hence a common factor.

e. 120 does not divide 144 therefore not a common factor.

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b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.