What is the remainder of 3^19 when divided by 10?

Question

A. 0
B. 1
C. 5
D. 7
E. 9

Vips0000 · Accepted Answer

Just look at how power of 3 works..

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 =243
.....

You'd notice that unit digit repeats itself after every 4 numbers.. In other words, 3^19 will have same unit number as 3^15, or 3^11 or 3^7 or 3^3....Which tells us, 3^19 has unit digit as 7..

Now, we know that any number with unit digit as 7 when divided by 10 will give u 7....

PS: Wrong section... Moving it to PS..

BG · Answer

3^19=3^4*3^4*3^4*3^4*3^3
3^4=81/10 has rmainder 1 
3^3=27/10 has remainder 7
1*1*1*1*7=7

buzzgaurav · Answer

I got D.
You can use the  Mod  function to solve this kind of problem.

mahesh004 · Answer

D it is...

3 ^ 16 will give remainder 1
3 ^ 3 will give remainder 7

so 7 * 1= 7

gidimba · Answer

I am getting 7 - D 

brute force to find the pattern in this case 39713971 and then just count to the 19th power we get 7

Luning1 · Answer

what is the remainder when 3^19 is divided by 10

The answer is 7 but I don't understand why. Is it as simple as 10-3?

shreyas · Answer

what is the remainder when 3^19 is divided by 10?

Units digit of 3^n (n = 1,2,3....) follows the following pattern: 3,9,7,1,3,9,7,1...
When divided by 10, the remainders would be 3,9,7,1,3,9,7,1...
3^19/10 -> remainder = 7

Temurkhon · Answer

we are interested in last digit of 3^19, so we should find circulation

3*1=3
3*2=9
3*3=7
3*4=1
3*5=3
circulation is 4, that means 19/4=4 with 3 remainder, so 7 is last digit. Dividing 10 gives us 7/10, so 7 is remainder

D

mvictor · Answer

I got D, and this is how I solved:
I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3

hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or 
^18 - units digit 9
and ^19 - units digit 7

therefore, when divided by 10, the remainder must be 7

PareshGmat · Answer

For  3^1 , remainder = 3

3^2 , remainder = 9

3^3 , remainder = 7

3^4 , remainder = 1

& so on........

For  3^{19} , remainder = 7

Answer = D

Abhishek009 · Answer

We know  \frac{3^4}{10}  = Reminder 1

3^19 =  \frac{(3^4)^4 *(3^3)}{10}

\frac{(3^4)^4}{10}  will have remainder 1

We need to find the reminder of  \frac{(3^3)}{10}

\frac{(3^3)}{10} =  \frac{(20 + 7)}{10}    => Reminder is 7

susheelh · Answer

The question is essentially asking - What is the unit digit of  3^{19}

Quick check on cycilicity of unit digit says

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

Therefore, the unit digit repeats after every 4th power of 3. For unit digit of  3^{19}  First find  Remainder \ of (\frac{19}{4})= 3 . The unit digit is 3rd term in the above sequence = 7

Answer is D

MathRevolution · Answer

3^{19}  =  (3^2)^{9}  * 3

=>  \frac{(3^2) }{ 10}  -> remainder = -1

=>  (-1)^9  = -1

=>  \frac{3 }{ 10}  -> remainder = -7

- 1 * - 7 = 7

Answer D

BrushMyQuant · Answer

What is the remainder of  3^{19}  when divided by 10

Theory: Remainder of a number by 10 is same as the unit's digit of the number

( Watch this Video  to Learn  How to find Remainders of Numbers by 10 )

Using Above theory Remainder of  3^{19}  by 10 = unit's digit of  3^{19}

Now to find the unit's digit of  3^{19} , we need to find the pattern / cycle of unit's digit of power of 3 and then generalizing it.

Unit's digit of  3^1  = 3
Unit's digit of  3^2  = 9
Unit's digit of  3^3  = 7
Unit's digit of  3^4  = 1
Unit's digit of  3^5  = 3

So, unit's digit of power of 3 repeats after every  4^{th}  number.
=> We need to divided 19 by 4 and check what is the remainder
=> 19 divided by 4 gives 3 remainder

=>  3^{19}  will have the same unit's digit as  3^3  = 7

So,  Answer will be D 
Hope it helps!

MASTER How to Find Remainders with 2, 3, 5, 9, 10 and Binomial Theorem

https://www.youtube.com/watch?v=h1HTEhmUb1w

ablatt4 · Answer

this can be retranslated to what is the units digit of 3^19

Lets see if we can find a pattern with 3^19

3^1/10 =r3
3^2/10=r9
3^3/10=r7
3^4/10=r1
3^5/10=r3
3^6/10=r9

clearly we have a pattern, if we need the 19th term we can see 19 will be the same as the 3 term so 7

D

What is the remainder of 3^19 when divided by 10?

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What is the remainder of 3^19 when divided by 10?

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