What is the units digit of 13^4*17^2*29^3?

Question

What is the units digit of  13^4*17^2*29^3 ?

(A) 9
(B) 7
(C) 5
(D) 3
(E) 1

nov79 · Accepted Answer

I think that the fastest and more important, the safest way to solve this is:
First brake the problem to three multiplication problems:
1. 13*13*13*13
2. 17*17
3. 29*29*29 
In all of the problems we don't have to multiply by the whole number, but only by the last digit (because that is what we are asked about).
Second, simply multiply: 13*13*13*13. It is actually 3*3*3*3 (we are interested in the last digit). Thus - 3*3=9, 9*3=7(the last digit), 7*3=1 (the last digit).
17*17 is actually 7*7 = 9 (the last digit).
29*29*29 is actually -9*9*9- that can be interpreted into 9*9=1 (the last digit) and 1*9=9.
So eventually we will have- 9 (29^3) * 9 (17^2) * 1 (13^4). Therefore - 9*9=1(the last digit), 1*1=1

So the correct answer is E -1.

Temurkhon · Answer

just need unit digit of every component and multipy them

3^1=3
3^2=9
3^3=7
3^4=1, it is first digit

7^2=9, it is second digit

9^3=9, it is third digit

1*9*9=1

E

gurpreetsingh · Answer

General rule :

To find the unit's digit- find the remainder when divided by 10.

to find the last two digits - find the remainder when divided by 100.

....and so on.

For advance theory of remainders check the Math book of gmat Club.

Abhishek009 · Answer

Units digit of 13^4 will be 1 Units digit of 17^2 will be 9 Units digit of 29^3 will be 9 So, Units digit of 13^4*17^2*29^3 will be 1 * 9 * 9 => 1 Answer will be option (E) 1 :lol:

BenLaz514 · Answer

Here's how you do this in under 1:30:

Step 1: Rephrase the question to --- (3^4) * (7^2) * (9^3)
Step 2: Apply unit digit power rules (ANEI = A number ending in) = (ANEI 1) * (ANEI 9) * (ANEI 9)
Step 3: Multiply the ends of numbers (i.e. units digits) = 1*9*9 = 81 = units digit of 1.

EgmatQuantExpert · Answer

Solution

Approach and Working:

The units digit of  13^4∗17^2∗29^3  will be same as the units digit of  3^4 * 7^2* 9^3 .
• Units digit of  3^4 * 7^2* 9^3 = Units digit of ( 3^4 )* Units digit of ( 7^2 ) * Units digit of ( 9^3 )
• = 1* 9*9= 1
Hence, the correct answer is option E.

Answer: E

atlas10 · Answer

To find the units digit of  13^4 * 17^2 * 29^3 , we only need to look at the units digits of the base numbers, which are 3, 7, and 9. So this becomes a units digit problem for  3^4 * 7^2 * 9^3 . The units digit of powers of 3 cycles every 4:  , so  3^4  ends in 1. For 7, the units digits cycle every 4:  , so  7^2  ends in 9. Powers of 9 alternate between 9 and 1:  , so  9^3  ends in 9. Now multiply the units digits:  1 * 9 = 9 , and  9 * 9 = 81 , so the final units digit is 1. Answer: (E).

akhilesh96 · Answer

1st take 13^4 take the last digit with power 3^4. 3 has cyclicity of 4 so divide power 4/4 and rem=0 then it is equal to 3^4 therefore 81 and 1 is the last digit. similarly 17^2 has to be taken as 7^2 and divide power 2/4 then rem is 2 therefore 7^2=49. 9 is the units digit. now for the last number 29^3 cyclicity of 9 is 2 { 9^1(odd power hence we get 9) 9^2( even power we get 81 hence 1 ) } again 9^3 odd power =9 unit digit.
hence from above multiply units digits 1*9*9=81 and finally 1 is the answer option E.

shivani1351 · Answer

Note: For finding the units digit, only focus on the last digit of every number. 
Let's find out the units digit of each tem individually:
Unit digit of 13^4 = 3*3*3*3 = 9*9 => 1
Unit digit of 17^2 = 7*7 => 9
Unit digit of 29^3 = 9*9*9 => 9

Effectively, the unit digit = 1*9*9 => 1

Hence, the correct answer is Option E (Ans)

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