What is the units digit of 20 21 22 23 24 251000?

20 21 22 23 24 251000 = 2^2 5 21 2 11 23 2^3 3 5^22^3 5^3 = 2^3 3 21 11 23 2^3 3^2 10 210.

jmc

number theory intermediate

Problem

What is the units digit of

\frac{20 \cdot 21 \cdot 22 \cdot 23 \cdot 24 \cdot 25}{1000}

Solution

\frac{20 \cdot 21 \cdot 22 \cdot 23 \cdot 24 \cdot 25}{1000} = \frac{2 ^{2} \cdot 5 \cdot 21 \cdot 2 \cdot 11 \cdot 23 \cdot 2 ^{3} \cdot 3 \cdot 5 ^{2}}{2 ^{3} \cdot 5 ^{3}} = 2^{3} \cdot 3 \cdot 21 \cdot 11 \cdot 23 \equiv 2^{3} \cdot 3^{2} (mod 10) \equiv 2 (mod 10)

Final answer