Question
Determine the unit digit of (23334 x
17724).Solution
ATQ,
Cyclicity of β3β = β4β (i.e. 3, 9, 7, 1) So, it repeats after every fourth power of β3β. Since, 23334 = 233(32 + 2) So, unit digit of 23334 = 9 And, cyclicity of β7β = β4β (i.e. 7, 9, 3, 1) So, it repeats after every fourth power of β7β. So, the unit digit of 17724 = 1 {Since, 24 is completely divisible by 4} So, required unit digit = 9 Γ 1 = 9
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