It is currently 20 Jan 2018, 09:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# To find the units digit of a large number?

Author Message
TAGS:

### Hide Tags

Director
Joined: 29 Nov 2012
Posts: 861

Kudos [?]: 1539 [1], given: 543

To find the units digit of a large number? [#permalink]

### Show Tags

03 Jul 2013, 21:58
1
KUDOS
1
This post was
BOOKMARKED
So if we are given a question what is the units digit of $$777^{777}$$

we find the pattern for 7 (7,9,3,1)

then we divide $$\frac{777}{4}$$ and the remainder is 1 so the units digit is $$7^1$$ which is 7?

Is this correct?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1539 [1], given: 543

Senior Manager
Joined: 24 Aug 2009
Posts: 492

Kudos [?]: 905 [0], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: To find the units digit of a large number? [#permalink]

### Show Tags

03 Jul 2013, 22:08
fozzzy wrote:
So if we are given a question what is the units digit of $$777^{777}$$

we find the pattern for 7 (7,9,3,1)

then we divide $$\frac{777}{4}$$ and the remainder is 1 so the units digit is $$7^1$$ which is 7?

Is this correct?

Absolutely Correct.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Kudos [?]: 905 [0], given: 276

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139569 [2], given: 12794

Re: To find the units digit of a large number? [#permalink]

### Show Tags

03 Jul 2013, 22:10
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
fozzzy wrote:
So if we are given a question what is the units digit of $$777^{777}$$

we find the pattern for 7 (7,9,3,1)

then we divide $$\frac{777}{4}$$ and the remainder is 1 so the units digit is $$7^1$$ which is 7?

Is this correct?

Yes.

The units digit of 777^777 = the units digit of 7^777.

7^1 has the units digit of 7;
7^2 has the units digit of 9;
7^3 has the units digit of 3;
7^4 has the units digit of 1.
7^5 has the units digit of 7 AGAIN.

The units digit repeats in blocks of 4: {7, 9, 3, 1}...

The remainder of 777/4 is 1, thus the units digit would be the first number from the pattern, so 7.

Hope it's clear.
_________________

Kudos [?]: 139569 [2], given: 12794

Director
Joined: 29 Nov 2012
Posts: 861

Kudos [?]: 1539 [0], given: 543

Re: To find the units digit of a large number? [#permalink]

### Show Tags

03 Jul 2013, 22:23
One final question here is another example

If we have the find the units digit of $$344^{328}$$

$$4^1$$ is 4
$$4^2$$ is 16
$$4^3$$ is 4

so the repeating block over here {4,6}

In this case the remainder is 0 so the units digit of this expression is 6?

so if there are 4 repeating blocks and the remainder is 0 we raise it to the 4th power ( some examples would be 3,7 etc) in this current example its the 2nd power?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1539 [0], given: 543

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139569 [1], given: 12794

Re: To find the units digit of a large number? [#permalink]

### Show Tags

03 Jul 2013, 22:26
1
KUDOS
Expert's post
fozzzy wrote:
One final question here is another example

If we have the find the units digit of $$344^{328}$$

$$4^1$$ is 4
$$4^2$$ is 16
$$4^3$$ is 4

so the repeating block over here {4,6}

In this case the remainder is 0 so the units digit of this expression is 6?

so if there are 4 repeating blocks and the remainder is 0 we raise it to the 4th power ( some examples would be 3,7 etc) in this case its the 2nd power?

Yes, if the remainder is 0, then take the last digit from the block.
_________________

Kudos [?]: 139569 [1], given: 12794

Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 602

Kudos [?]: 505 [2], given: 17

Re: To find the units digit of a large number? [#permalink]

### Show Tags

07 Jul 2013, 20:00
2
KUDOS
Expert's post
fozzy,

you are correct in both cases. here is how i like to think about it:
7^{777} example:
If we divide 777 by 4, the quotient is 194 and the remainder is 1.
This means that we will have 194 of {7, 9, 3, 1} repeating blocks, and we will have 1 more term left, and the units digit of 7^{777} will be 7, the first term in the repeating block.

When we look at the case of 344^{328}, the units digit of powers of 4 cycle as {4, 6}, when we divide 328 by 2, the remainder is 0, this means that there will be exactly 164 blocks consisting of {4,6} without any remainder and the units digit of 344^{328} will be 6.

here are problems using the same concept(some hard):
#1) if-n-is-a-positive-integer-what-is-the-remainder-when-82380.html
#2) what-is-the-remainder-when-7-345-7-11-2-is-divided-by-26794.html
#3) remainder-when-7-4n-3-6-n-104848.html
#4) if-3-4n-1-is-divided-by-10-can-the-remainder-be-0-a-4662.html
#5) what-s-the-remainder-of-2-x-divided-by-10-1-x-is-an-even-9651.html

cheers,
dabral

Kudos [?]: 505 [2], given: 17

Non-Human User
Joined: 09 Sep 2013
Posts: 14217

Kudos [?]: 291 [0], given: 0

Re: To find the units digit of a large number? [#permalink]

### Show Tags

16 Mar 2015, 15:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Intern
Joined: 01 Apr 2015
Posts: 9

Kudos [?]: 3 [0], given: 2

Re: To find the units digit of a large number? [#permalink]

### Show Tags

01 Apr 2015, 23:35
Finding the UNIT’S DIGIT - please share some more useful tricks if its there.
_________________

Founder, aptiDude
"Get useful study materials at aptiStore!"

Kudos [?]: 3 [0], given: 2

Non-Human User
Joined: 09 Sep 2013
Posts: 14217

Kudos [?]: 291 [0], given: 0

Re: To find the units digit of a large number? [#permalink]

### Show Tags

20 Nov 2016, 06:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 14217

Kudos [?]: 291 [0], given: 0

Re: To find the units digit of a large number? [#permalink]

### Show Tags

04 Dec 2017, 14:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Re: To find the units digit of a large number?   [#permalink] 04 Dec 2017, 14:10
Display posts from previous: Sort by