The greatest number of arrangements using every balloon is an illustration of the highest common factors (HCF).
The greatest number of arrangements you can make using every balloon is 8.
Given that:
[tex]White = 16[/tex]
[tex]Red = 24[/tex]
To determine the greatest number of arrangements, we simply calculate the HCF of 16 and 24.
We have:
[tex]16 = 2\times 2\times 2 \times 2[/tex]
[tex]24 = 2\times 2\times 2 \times 3[/tex]
The highest common factor is:
[tex]HCF =2 \times 2 \times 2[/tex]
[tex]HCF =8[/tex]
Hence, the greatest number of arrangements you can make using every balloon is 8.
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