# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.108)

108.

What is the unit digit in (4137)754?

 [A]. 1 [B]. 3 [C]. 7 [D]. 9

Explanation:

Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}

=Unit digit in { 292915317923361 x 17114769 }

= (1 x 9) = 9

 Avinash said: (Aug 19, 2010) Just devide the power with 4, we get the remainder 2 and if we observe the last digits in the first four consecutive powers of 7, we get 7,9,3,1, and after that last digits will repeat again, that is every period of 4, the last digits will be repeated. So, as we got the remainder 2 when we divide the power by 4 the last digit would be 9. There is no need to expand 4173^2.

 Rammurti Rawat said: (Oct 16, 2010) No need to this question please explain again?

 Nav said: (Aug 19, 2013) 754 => 4*n + 2, Here n will be 188. So, unit digit will be the unit digit of 7^2, ie 9.

 Narasingarao said: (Oct 5, 2013) Is it always that the powers are divided by 4? If yes, kindly explain the concept.

 Manish Methani said: (Jun 8, 2014) No dude not always by 4. 4 ka first power = 4 (unit digit 4). 4 ka square = 16 ( unit digit 6). 4 ka cube = 64. ( unit digit 4). 4 ka fourth power = 2401 ( unit digit 1). 4 ka fifth power = now check unit digits later on going to be repeat again. That is 4,6,4,1. That's why. Unit digit restriction. Is. Upto 4th power in this case That's why.. Divide the no by 754 by 4.. you will get 2 as a remainder. By rule , Dividend = divisor *quotient +remainder. Assume quotient = n. 754=4n+2. n=188. 4137 power 754 = 7 ^ 4 ^188 + 7^2. =9.

 Fazz said: (Aug 25, 2014) Power = 754. Divide by 4(7,9,3,1). 754/4 = 2(remainder). Given number 4137 = 7(last digit). Last digit^remainder. 7^2 = 49. Last digit of 49 is 9(answer).

 Anki said: (Mar 27, 2015) 2^4344 what will be unit digit here?

 Khushi said: (Jun 20, 2015) Please explain how to find unit digit in any problem?

 Aditya said: (Jul 3, 2015) Why it can't be solve like this (4137)^754? As 7^4 as equal to 1.

 Mohan S said: (Jul 29, 2016) @Manish Methani. How 4 To the power 4 is 2401? Just explain.

 Krishna said: (Aug 10, 2016) The units will be like. 7^1=7. 7^2=49; unit dig=9, For 7^3 = 343; uit dig=3. For 7^4=___1 (unit dig =1). Then it follows as. 7, 9, 3, 1 consecutively. Here we have cycles of 4. Therefore, 752 can be divided from 4. 752 = 1. 753 = 7. 754 = 9; by using the cycle the answer is 9.

 Satpreet said: (Feb 3, 2017) If we consider (4137^2) ^377 is it right or is there compulsory to consider 4 as the power?

 Arvind said: (Sep 28, 2019) What will be the unit number of (3^57*6^41*7^63)?

 Md Aftab Alam said: (Oct 9, 2019) @Manish. 4 ka 4th power =256 not 2401.