Explanation

Since 10 ≡ 3 (mod 7), we get 10³ ≡ 27 ≡ 6 and 10⁶ ≡ 36 ≡ 1 (mod 7). Writing 20 = 6×3+2 gives 10²⁰ = (10⁶)³·10² ≡ 1³·2 = 2 (mod 7). Hence the remainder on dividing 10²⁰ by 7 is 2.