Find the unit digit of (432)412 × (499)431.

  1. 2
  2. 4
  3. 6
  4. 8

Answer (Detailed Solution Below)

Option 2 : 4
Free
RRB Exams (Railway) Biology (Cell) Mock Test
8.9 Lakh Users
10 Questions 10 Marks 7 Mins

Detailed Solution

Download Solution PDF

Given:

(432)412 × (499)431

Concept:

9even no. = unit digit 1

9odd no. = unit digit 9

Calculation:

(432)412 × (499)431

Taking unit digits

⇒ 2412 × 9431

As we know unit digit of 21 = 2, 22 = 4, 23 = 8, 24 = 6

⇒ 24(103) × 9431

⇒ 6 × 9

⇒ 54

The unit digit of (432)412 × (499)431 is 4.

Additional Information Sunny 28.7.21

To determine the last digit of the number 432412, we need to focus on the last digit of base 432 i.e. 2 and the exponential part 412.

We know,

Power of 2

Last digit

21

2

22

4

23

8

24

6

25

2

26

4

27

8

28

6

29

2


Notice the pattern of the last digit. It is 2, 4, 8, 6, 2, 4, 8, 6, 2 …… so on.

Thus the last digit is repetitive and is a four-digit long i.e. 1, 2, 8, 6. If we keep on writing this table till the power of 2 reaches 412 then how many times this pattern repeated can be found by dividing 412 by 4.

412 divided by 4 is 103 with remainder 0 which indicates that the pattern gets fully repeated 412 times and then ends up with the digit i.e. 4. (if it is fully divisible we take power as 4)

∴ The Last digit of the number 432412 is 6.

9even no. = unit digit 1

9odd no. = unit digit 9

∴ The Last digit of the number 9431 is 9

 The unit digit of (432)412 × (499)431 is 4.

Latest RRB NTPC Updates

Last updated on Jul 5, 2025

-> RRB NTPC Under Graduate Exam Date 2025 has been released on the official website of the Railway Recruitment Board. 

-> The RRB NTPC Admit Card will be released on its official website for RRB NTPC Under Graduate Exam 2025.

-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here. 

-> The RRB NTPC 2025 Notification released for a total of 11558 vacancies. A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.

-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.

-> Prepare for the exam using RRB NTPC Previous Year Papers.

-> Get detailed subject-wise UGC NET Exam Analysis 2025 and UGC NET Question Paper 2025 for shift 1 (25 June) here

Get Free Access Now
Hot Links: teen patti rummy 51 bonus teen patti master apk download teen patti gold new version teen patti club teen patti vip