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Sub 505 Level|   Exponents|   Remainders|            
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XxxyyY
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What is the remainder of 3^19 when divided by 10? 27 May 2006, 22:53
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

85% (00:50) correct 15% (01:09) wrong based on 823 sessions

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

A. 0
B. 1
C. 5
D. 7
E. 9
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D
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What is the remainder of 3^19 when divided by 10? 07 Feb 2014, 17:15
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Luning1
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?

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..
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What is the remainder of 3^19 when divided by 10? 27 May 2006, 23:17
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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
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What is the remainder of 3^19 when divided by 10? 27 May 2006, 23:17
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I got D.
You can use the Mod function to solve this kind of problem.
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What is the remainder of 3^19 when divided by 10? 27 May 2006, 23:21
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D it is...

3 ^ 16 will give remainder 1
3 ^ 3 will give remainder 7

so 7 * 1= 7
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What is the remainder of 3^19 when divided by 10? 31 May 2006, 18:12
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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
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What is the remainder of 3^19 when divided by 10? 07 Feb 2014, 17:06
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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?
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What is the remainder of 3^19 when divided by 10? 07 Feb 2014, 19:29
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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
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What is the remainder of 3^19 when divided by 10? 10 Sep 2014, 21:52
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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
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What is the remainder of 3^19 when divided by 10? 12 Sep 2014, 11:48
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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
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What is the remainder of 3^19 when divided by 10? 30 Sep 2014, 23:23
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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
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What is the remainder of 3^19 when divided by 10? 14 Nov 2015, 12:21
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X & Y
What is the remainder of 3^19 when divided by 10?

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

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 \(\frac{(3^3)}{10}\)

\(\frac{(3^3)}{10} = [m]\frac{(20 + 7)}{10}\) => Reminder is 7
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What is the remainder of 3^19 when divided by 10? 30 Jun 2017, 20:49
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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
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What is the remainder of 3^19 when divided by 10? 01 Sep 2020, 02:33
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\(3^{19}\) = \((3^2)^{9}\) * 3

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

=> \((-1)^9\) = -1

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

- 1 * - 7 = 7

Answer D
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What is the remainder of 3^19 when divided by 10? Updated on: 16 Sep 2024, 04:49
Originally posted by BrushMyQuant on 07 Sep 2022, 12:01.
Last edited by BrushMyQuant on 16 Sep 2024, 04:49, edited 1 time in total.
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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

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What is the remainder of 3^19 when divided by 10? 02 Feb 2023, 14:05
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I started counting from 3^0 and I got 9 as an answer, how do I know if I have to start from 3^0 or 3^1?

help
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What is the remainder of 3^19 when divided by 10? 31 May 2024, 09:16
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