Yes
No

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By prime factorisation we find :

8! = 1 × 2^7 × 3^2 × 5 × 7

So let's start our calcul with :

1 + 5 + 7

Because if any of these integers is multiplied by any other, the result is at least a 2 digit number (except for "1" but if i'm correct, it has to stay as "1" and can't be removed)

Then, 36 is even, thus we know that 3^2 has to be as 9 in our calcul (not 6 and 6), else the sum can't be even. So we get :

1 + 5 + 7 + 9

Then there only stay 2^7 which has to be decompsed into four 1 digit numbers. So we can first try :

1 + 5 + 7 + 9 + 2 + 2 + 4 + 8 = 38

Then we just have to adjust a little bit to finally get :

1 + 5 + 7 + 9 + 2 + 4 + 4 + 4 = 36

1 × 5 × 7 × 9 × 2 × 4 × 4 × 4 = 8!