Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 01 Sep 2016
Posts: 18

Re: Math: Number Theory
[#permalink]
Show Tags
27 Oct 2016, 01:30
• Any positive divisor of n is a product of prime divisors of n raised to some power.
pls someone explain with example



Math Expert
Joined: 02 Sep 2009
Posts: 61549

Re: Math: Number Theory
[#permalink]
Show Tags
27 Oct 2016, 02:59
sanaexam wrote: • Any positive divisor of n is a product of prime divisors of n raised to some power.
pls someone explain with example For example, say n = 72. Consider it's factor 36 > \(36 = 2^2*3^2\) > 36 = product of prime divisors of n raised to some power.
_________________



MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2940
GPA: 4
WE: Engineering (Computer Software)

Re: Math: Number Theory
[#permalink]
Show Tags
23 May 2017, 15:47
Bunuel wrote: NUMBER THEORY
Fractions (also known as rational numbers) can be written as terminating (ending) or repeating decimals (such as 0.5, 0.76, or 0.333333....).
 0.333333... looks like a recurring decimal and is not a rational number. This can be better modified as 0.33333 etc so it is less confusing in my opinion.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 61549

Re: Math: Number Theory
[#permalink]
Show Tags
24 May 2017, 03:02
workout wrote: Bunuel wrote: NUMBER THEORY
Fractions (also known as rational numbers) can be written as terminating (ending) or repeating decimals (such as 0.5, 0.76, or 0.333333....).
 0.333333... looks like a recurring decimal and is not a rational number. This can be better modified as 0.33333 etc so it is less confusing in my opinion. 0.333333... IS a rational number because it equals to the ratio of two integers: 1/3 = 0.3333......
_________________



Director
Joined: 06 Jan 2015
Posts: 733
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: Math: Number Theory
[#permalink]
Show Tags
28 Feb 2018, 17:18
Adding Few Formulas Sum of First "n" natural nos = n(n+1)/2 Sum of First "n" ODD natural nos = n^2 Sum of First "n" EVEN natural nos = n (n+1)
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution



Intern
Joined: 20 Dec 2014
Posts: 34

Re: Math: Number Theory
[#permalink]
Show Tags
27 Mar 2018, 04:40
Hi BunuelThe topic doesn’t touch up on LCM and HCF for fractions.. LCM( (a/b) , (c/d) ) = LCM(a,c)/HCF(b,d)) HCF( (a/b) , (c/d) ) = HCF(a,c)/LCM(b,d) Please add if tested on GMAT. Question from where I started to look for the theory: https://gmatclub.com/forum/whatisthe ... ml#p818818



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1389
Location: India
WE: Engineering (Other)

Re: Math: Number Theory
[#permalink]
Show Tags
04 May 2018, 03:45
Bunuel niks18 gmatbusters pushpitkc VeritasPrepKarishmaI have a small query regarding rounding: How do I interpret nearest ten, nearest hundred etc in 1234.1234 on both LHS and RHS of decimal?
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!



Retired Moderator
Joined: 27 Oct 2017
Posts: 1491
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Math: Number Theory
[#permalink]
Show Tags
04 May 2018, 05:03
Hii You have asked regarding rounding to nearest tens, hundred for 1234.1234 on both LHS and RHS of decimal. First of all , Lets know what does the place signify: we denote the digits as units, tens, hundreds, thousands before decimal and tenth, hundredth after decimal. see the sketch Attachment:
gmatbusters3.jpg [ 27.32 KiB  Viewed 2649 times ]
Rounding Simplifying a number to a certain place value. Drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep. It means if we round 47 to nearest ten = 50 whereas, 44 to nearest ten = 40 Now lets come to your question: 1234.1234 Rounding to nearest ten = 1230 Rounding to nearest hundred = 1200 Rounding to nearest tenth =1234.1 Rounding to nearest hundredth= 1234.12 I hope it is clear now. Fell free to tag again. adkikani wrote: I have a small query regarding rounding:
How do I interpret nearest ten, nearest hundred etc in
1234.1234
on both LHS and RHS of decimal?
_________________



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1389
Location: India
WE: Engineering (Other)

Re: Math: Number Theory
[#permalink]
Show Tags
04 May 2018, 05:56
gmatbusters Thanks for the pic , that made me wonder if the difference in position of tens on LHS and RHS is because of raising base of 10 to exponents say 0,1 and 1. Is this how we arrive at PLACE VALUES for a number? Sorry, coming from engineering bakground, am still not able to erase why aspects of logic
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!



Retired Moderator
Joined: 27 Oct 2017
Posts: 1491
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Math: Number Theory
[#permalink]
Show Tags
04 May 2018, 06:03
yes you got it right Attachment:
GB.jpg [ 50.21 KiB  Viewed 2631 times ]
adkikani wrote: gmatbusters Thanks for the pic , that made me wonder if the difference in position of tens on LHS and RHS is because of raising base of 10 to exponents say 0,1 and 1. Is this how we arrive at PLACE VALUES for a number? Sorry, coming from engineering bakground, am still not able to erase why aspects of logic
_________________



Intern
Joined: 21 Sep 2018
Posts: 2

Re: Math: Number Theory
[#permalink]
Show Tags
06 Oct 2018, 21:02
I just started looking at this and I'm impressed. I have a suggestion for the LCM section. I believe it should be changed as follows, but please correct me if I'm wrong... "Lowest Common Multiple  LCM
The lowest common multiple orlowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b. Since it is a multiple, it can be divided by a and b without a remainder. If either a or b is 0, so that there is no such positive integer, then lcm(a, b) is defined to be zero.
To find the LCM, you will need to do primefactorization. Then multiply all the factors. (For any factors that are common, use the highest power.)"



Manager
Joined: 12 Jul 2018
Posts: 63
Location: India
GMAT 1: 420 Q26 V13 GMAT 2: 540 Q44 V21

Re: Math: Number Theory
[#permalink]
Show Tags
30 Nov 2018, 23:13
Can someone please explain me the last digit concept using more examples?
LAST DIGIT OF A PRODUCT Last digits of a product of integers are last digits of the product of last digits of these integers. For instance last 2 digits of 845*9512*408*613 would be the last 2 digits of 45*12*8*13=540*104=40*4=160=60 Example: The last digit of 85945*89*58307=5*9*7=45*7=35=5?



Intern
Joined: 04 Sep 2018
Posts: 26
GPA: 3.33

Re: Math: Number Theory
[#permalink]
Show Tags
09 Dec 2018, 08:55
Hi. Is it possible to solve official questions related to this specific topic "Numbers Theory", after going over this topic here? So, for instance, let's say we read the topic "Percents" from the below link. Ideally, want to solve questions related to each topic as I study through. Just want to know if something like that is a possibility on the forum. https://gmatclub.com/forum/allyouneed ... l#p1130136Thanks in advance. Cheers.



Current Student
Joined: 04 Jun 2018
Posts: 155
GMAT 1: 610 Q48 V25 GMAT 2: 690 Q50 V32 GMAT 3: 710 Q50 V36

Re: Math: Number Theory
[#permalink]
Show Tags
08 Jan 2019, 06:15
Exponents and divisibility: a^n−b^n is ALWAYS divisible by a−b a^n−b^n is divisible by a+b if n is even. a^n+b^n is divisible by a+b if n is odd, and not divisible by a+b if n is even. Hi Can some expert please explain this concept more clearly. What I am looking for is the proof of these statements. BunuelVeritasKarishmachetan2uGladiator59gmatbustersMathRevolutionAjiteshArun



Math Expert
Joined: 02 Aug 2009
Posts: 8254

Re: Math: Number Theory
[#permalink]
Show Tags
08 Jan 2019, 06:50
nitesh50 wrote: Exponents and divisibility: a^n−b^n is ALWAYS divisible by a−b a^n−b^n is divisible by a+b if n is even. a^n+b^n is divisible by a+b if n is odd, and not divisible by a+b if n is even. Hi Can some expert please explain this concept more clearly. What I am looking for is the proof of these statements. BunuelVeritasKarishmachetan2uGladiator59gmatbustersMathRevolutionAjiteshArunHi nitesh, It is to do with binomial theorem, which further deals with expansion of a term.. Say you are looking for a^n . I can write a = ab+b.. \(a^n=(ab+b)^n=((ab)+b)^n = (ab)^n+n(ab)^{n1}b^1+....+b^n.....a^nb^n=(ab)^n+n(ab)^{n1}b^1+...=(ab)((ab)^{n1}+.........)\) So, Right hand side is multiple of ab and on left side we have a^nb^n.. so a^nb^n is a multiple of ab similarly for the other too.. Just take small values to confirm.. Let n = 4.. \(a^4b^4=(a^2b^2)(a^2+b^2)=(ab)(a+b)(a^2+b^2)\).. so multiple of ab and a+b. Let n = 3... \(a^3b^3=(ab)(a^2+ab+b^2)\)... so multiple of only ab
_________________



Retired Moderator
Joined: 27 Oct 2017
Posts: 1491
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Math: Number Theory
[#permalink]
Show Tags
08 Jan 2019, 06:56
The remainder /factor theorem If you divide a polynomial f(x) by (x  h), then the remainder is f(h). Hence if f(h) is 0, remainder = 0. hence (xh) is a factor of f(x). Attachment:
Factor theorem.jpg [ 79.42 KiB  Viewed 1401 times ]
nitesh50 wrote: Exponents and divisibility: a^n−b^n is ALWAYS divisible by a−b a^n−b^n is divisible by a+b if n is even. a^n+b^n is divisible by a+b if n is odd, and not divisible by a+b if n is even. Hi Can some expert please explain this concept more clearly. What I am looking for is the proof of these statements. BunuelVeritasKarishmachetan2uGladiator59gmatbustersMathRevolutionAjiteshArun
_________________



Intern
Joined: 18 Oct 2018
Posts: 18
Location: India

Re: Math: Number Theory
[#permalink]
Show Tags
29 Mar 2019, 00:11
• If a is a factor of b and b is a factor of a, then a=b or a=−b.
I did not understand this. Could you please explain?



Retired Moderator
Joined: 27 Oct 2017
Posts: 1491
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Math: Number Theory
[#permalink]
Show Tags
29 Mar 2019, 00:44
It means a/b is an integer Also, b/a is an integer. This is only possible if either a=b or a=b. Hope, it is clear now. dee1711s wrote: • If a is a factor of b and b is a factor of a, then a=b or a=−b.
I did not understand this. Could you please explain? Posted from my mobile device
_________________



Intern
Joined: 26 Mar 2019
Posts: 6

Re: Math: Number Theory
[#permalink]
Show Tags
01 Apr 2019, 23:28
• If a number equals the sum of its proper divisors, it is said to be a perfect number. Example: The proper divisors of 6 are 1, 2, and 3: 1+2+3=6, hence 6 is a perfect number.
There are some elementary rules: • If aa is a factor of bb and aa is a factor of cc, then aa is a factor of (b+c)(b+c). In fact, aa is a factor of (mb+nc)(mb+nc) for all integers mm and nn.
• If aa is a factor of bb and bb is a factor of cc, then aa is a factor of cc.
• If aa is a factor of bb and bb is a factor of aa, then a=ba=b or a=−ba=−b.
• If aa is a factor of bcbc, and gcd(a,b)=1gcd(a,b)=1, then a is a factor of cc.
• If pp is a prime number and pp is a factor of abab then pp is a factor of aa or pp is a factor of bb.
PLEASE CAN YOU EXPLAIN ABOUT THE ABOVE WITH EXAMPLES?



Math Expert
Joined: 02 Sep 2009
Posts: 61549

Re: Math: Number Theory
[#permalink]
Show Tags
01 Apr 2019, 23:29
KarthikaD wrote: • If a number equals the sum of its proper divisors, it is said to be a perfect number. Example: The proper divisors of 6 are 1, 2, and 3: 1+2+3=6, hence 6 is a perfect number.
There are some elementary rules: • If aa is a factor of bb and aa is a factor of cc, then aa is a factor of (b+c)(b+c). In fact, aa is a factor of (mb+nc)(mb+nc) for all integers mm and nn.
• If aa is a factor of bb and bb is a factor of cc, then aa is a factor of cc.
• If aa is a factor of bb and bb is a factor of aa, then a=ba=b or a=−ba=−b.
• If aa is a factor of bcbc, and gcd(a,b)=1gcd(a,b)=1, then a is a factor of cc.
• If pp is a prime number and pp is a factor of abab then pp is a factor of aa or pp is a factor of bb.
PLEASE CAN YOU EXPLAIN ABOUT THE ABOVE WITH EXAMPLES? ____________________________ Explained on previous pages.
_________________




Re: Math: Number Theory
[#permalink]
01 Apr 2019, 23:29



Go to page
Previous
1 2 3 4 5
Next
[ 81 posts ]



