Question 32

Statement 1 - Number of factors of 2018 is 2<br>Statement 2 - Sum of the squares of the factors of 2018 is 1018085

Solution

$$2018 = 2 \times 1009$$ with 1009 prime, so its factors are 1, 2, 1009, 2018, which is 4 factors; Statement 1 is false. The sum of their squares is $$(1 + 2^2)(1 + 1009^2) = 5 \times 1018082 = 5090410$$, not 1018085, so Statement 2 is false. Hence options b and d are both correct.

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