Happy 2018, Brilliant!

Number Theory Level 2

2018 \Huge { \color{gold}2018 } Find the sum of the distinct prime factors of the number above.


The answer is 1011.

Steven Yuan by Steven Yuan , 20, USA

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2 solutions

Steven Yuan
Jan 1, 2018

2018 = 2 × 1009. 2018 = 2 \times 1009.

1009 is prime because no prime less than 1009 ≈ 31.7 \sqrt{1009} \approx 31.7 divides into 1009 evenly.

Thus, the sum of the distinct prime factors of 2018 is 2 + 1009 = 1011 . 2 + 1009 = \boxed{1011}.

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Munem Shahriar
Jan 1, 2018

2018 has 4 divisors: 1,2,1009 and 2018. Where 2 and 1009 are prime numbers.

2018 = 2 × 1009 2018 = 2 \times 1009

Hence 2 + 1009 = 1011 2+1009 = \boxed{1011}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

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