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Question 6
If $$56 \times 75 \times 60 \times 84 \times 210 = 2^p \times 3^q \times 5^r \times 7^s$$, then what is the value of $$\left[\frac{(p + q)}{s}\right] + r$$?
Solution
Writing each of the numbers in terms of prime factors we have
=7*2*2*2*3*5*5*2*2*5*3*2*2*3*7*5*3*2*7
=$$2^{8}*3^{4}*5^{4}*7^{3}$$
p=8 q=4 r=4 s=3
=Â $$\left[\frac{(p + q)}{s}\right] + r$$
=4+4
=8
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