Question:
Find the unit digit of \(3^{65} \times 6^{59} \times 7^{71}\).
\(3^{65} \times 6^{59} \times 7^{71}\) का इकाई अंक ज्ञात कीजिए।
Options:
- 4
- 2
- 6
- 8
- 4
- 2
- 6
- 8
Correct Answer: a)
Explanation:
– For \(3^{65}\): cyclicity is 4. \(65 \pmod 4 = 1 \implies 3^1 = 3\).
– For \(6^{59}\): unit digit of any power of 6 is always 6.
– For \(7^{71}\): \(71 \pmod 4 = 3 \implies 7^3 = 343 \implies 3\).
Unit digit = \((3 \times 6 \times 3) = 54 \implies 4\).
– For \(6^{59}\): unit digit of any power of 6 is always 6.
– For \(7^{71}\): \(71 \pmod 4 = 3 \implies 7^3 = 343 \implies 3\).
Unit digit = \((3 \times 6 \times 3) = 54 \implies 4\).
इकाई अंक: \(3^1 \times 6 \times 7^3 = 3 \times 6 \times 3 = 54\), अतः इकाई अंक 4 है।