Factorial!

Number Theory Level 3

The ten's digit in 1 ! 1! + 4 ! 4! + 7 ! 7! + 10 ! 10! + 12 ! 12! + 13 ! 13! + 15 ! 15! is divisible by

5 6 7 4

Gaurav Singh by Gaurav singh , 21, India

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1 solution

Ankit Nigam
Apr 17, 2016

1 ! + 4 ! + 7 ! + 10 ! + 12 ! + 13 ! + 15 ! ( m o d 100 ) ≡ 1 + 24 + 40 = 65 ( m o d 100 ) 1! + 4! + 7! + 10! + 12! + 13! + 15! \pmod{100} \equiv 1 + 24 + 40 = 65 \pmod{100} because 10 ! 10! and above factorials will have greater than 1 trailing zeroes. So tens digit is 6 \boxed{6}

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