5

Part of 2008 Regional Olympiad of Mexico Center Zone

Problems(1)

max prime that divides S = p_1 + p_2 + p_3 + ...+ p_ {999}, product of digits

Source: Mathematics Regional Olympiad of Mexico Center Zone 2008 P5

Each positive integer number

n \ ge 1

is assigned the number

p_n

which is the product of all its non-zero digits. For example,

p_6 = 6

p_ {32} = 6

p_ {203} = 6

S = p_1 + p_2 + p_3 + \dots + p_ {999}

. Find the largest prime that divides

S

number theoryProductDigitsdivides