Question : What is the unit digit of $(217)^{413} imes (819)^{547} imes (414)^{624} imes (342)^{812}$?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 8

Question

Question : What is the unit digit of $(217)^{413} imes (819)^{547} imes (414)^{624} imes (342)^{812}$?

Option 1: 2

Option 2: 4

Option 3: 6

Option 4: 8

Team Careers360 · Accepted Answer

Correct Answer: 8

Solution : Given:
(217)⁴¹³ × (819)⁵⁴⁷ × (414)⁶²⁴ × (342)⁸¹²
Solution:
The cyclicity of 7 is 4.
The cyclicity of 9 is 2.
The cyclicity of 4 is 2.
The cyclicity of 2 is 4.
According to the cyclicity theorem, divide the powers by 4 and take reminders. Otherwise, take 4.
The unit digit of (217)⁴¹³ = 7⁴¹³ = 7^{(4 × 103) + 1} = 7¹ = 7
The unit digit of (819)⁵⁴⁷ = 9⁵⁴⁷ = 9^{(2 × 273) + 1} = 9¹ = 9
The unit digit of (414)⁶²⁴ = 4⁶²⁴ = 4^{(2 × 312)} = 4⁴ = 6
The unit digit of (342)⁸¹² = 2⁸¹² = 2^{(4 × 203)} = 2⁴ = 6
The unit digit of the given expression will be the same as the unit digit of 7⁴¹³ × 9⁵⁴⁷ × 4⁶²⁴ × 2⁸¹²
⇒ 7¹ × 9³ × 4⁴ × 2⁴
For unit digit ⇒ 7 × 9 × 6 × 6
$ herefore$ The required unit digit = 8
Hence, the correct answer is 8.

Popular Searches

Question : What is the unit digit of $(217)^{413}\times (819)^{547}\times (414)^{624}\times (342)^{812}$?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 8

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Question : Directions: By Interchanging the given two numbers which of the following equations will be correct?
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Option 1: 8 ÷ 1 + 4 × 2 – 3 = 18
Option 2: 7 × 2 + 6 ÷ 3 – 8 = 60
Option 3: 2 × 4 – 8 + 6 ÷ 3 = 33
Option 4: 8 × 4 + 6 – 2 ÷ 1 = 6

Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct?
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Option 1: 7 + 3 – 4 ÷ 2 × 8 = 9
Option 2: 6 ÷ 2 × 8 + 3 – 1 = 17
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Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct?
× and +, 6 and 4
Option 1: 3 × 9 – 4 ÷ 2 + 6 = 8
Option 2: 8 × 6 + 4 ÷ 2 – 5 = –5
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Option 4: 7 × 6 – 4 + 9 ÷ 3 = –7

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Question : What is the unit digit of $(217)^{413}\times (819)^{547}\times (414)^{624}\times (342)^{812}$?Option 1: 2Option 2: 4Option 3: 6Option 4: 8

Related Questions

Question : The units digit in $3 × 38 ×537 × 1256$ is:Option 1: 4Option 2: 2Option 3: 6Option 4: 8

Question : The value of $4 \div 12$ of $[3 \div 4$ of $\{(4-2) \times 6 \div 2\}]-2 \times 6 \div 8+3$ is:Option 1: $4 \frac{1}{6}$Option 2: $3 \frac{1}{3}$Option 3: $2 \frac{1}{3}$Option 4: $7 \frac{1}{6}$

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Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 3 and 8Option 1: 7 + 3 – 4 ÷ 2 × 8 = 9Option 2: 6 ÷ 2 × 8 + 3 – 1 = 17Option 3: 8 – 3 + 6 × 2 ÷ 4 = -2Option 4: 2 + 3 – 6 ÷ 2 × 8 = 1

Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? × and +, 6 and 4Option 1: 3 × 9 – 4 ÷ 2 + 6 = 8Option 2: 8 × 6 + 4 ÷ 2 – 5 = –5Option 3: 8 – 3 × 6 + 4 ÷ 1 = 18Option 4: 7 × 6 – 4 + 9 ÷ 3 = –7