Question : Which of the following numbers is not a factor of $5^p7^q,(p\neq 0,q\neq 0)$?
Option 1: 35
Option 2: 175
Option 3: 1225
Option 4: 735
Correct Answer: 735
Solution :
Checking the factors of all the options for divisibility by 5 and 7.
35 = 5 × 7
175 = 5 × 5 × 7
1225 = 5 × 5 × 7 × 7
735 = 5 × 7 × 7 × 3
735 has a factor of 3 other than 5 and 7.
$\therefore$ 735 is not a factor of $5^p7^q$.
Hence, the correct answer is 735.
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