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Re: Math: Number Theory
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 27 Oct 2016, 02:30
• Any positive divisor of n is a product of prime divisors of n raised to some power.
pls someone explain with example
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Re: Math: Number Theory
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27 Oct 2016, 03:59
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.
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Re: Math: Number Theory
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23 May 2017, 16:47
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.
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Re: Math: Number Theory
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24 May 2017, 04:02
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......
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Re: Math: Number Theory
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28 Feb 2018, 18:18
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)
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Re: Math: Number Theory
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27 Mar 2018, 05:40
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/what-is-the- ... ml#p818818
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Re: Math: Number Theory
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04 May 2018, 04:45
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?
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Re: Math: Number Theory
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04 May 2018, 06:03
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 1711 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?
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Re: Math: Number Theory
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04 May 2018, 06:56
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  _________________
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Re: Math: Number Theory
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04 May 2018, 07:03
yes you got it right Attachment: 
GB.jpg [ 50.21 KiB | Viewed 1694 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
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Re: Math: Number Theory
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06 Oct 2018, 22:02
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 prime-factorization. Then multiply all the factors. (For any factors that are common, use the highest power.)"
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Re: Math: Number Theory
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01 Dec 2018, 00:13
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?
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Re: Math: Number Theory
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09 Dec 2018, 09:55
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/all-you-need ... l#p1130136Thanks in advance. Cheers.
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Re: Math: Number Theory
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08 Jan 2019, 07:15
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
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Re: Math: Number Theory
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08 Jan 2019, 07:50
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 = a-b+b.. \(a^n=(a-b+b)^n=((a-b)+b)^n = (a-b)^n+n(a-b)^{n-1}b^1+....+b^n.....a^n-b^n=(a-b)^n+n(a-b)^{n-1}b^1+...=(a-b)((a-b)^{n-1}+.........)\) So, Right hand side is multiple of a-b and on left side we have a^n-b^n.. so a^n-b^n is a multiple of a-b similarly for the other too.. Just take small values to confirm.. Let n = 4.. \(a^4-b^4=(a^2-b^2)(a^2+b^2)=(a-b)(a+b)(a^2+b^2)\).. so multiple of a-b and a+b. Let n = 3... \(a^3-b^3=(a-b)(a^2+ab+b^2)\)... so multiple of only a-b
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Re: Math: Number Theory
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08 Jan 2019, 07:56
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 (x-h) is a factor of f(x).  Attachment: 
Factor theorem.jpg [ 79.42 KiB | Viewed 282 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_________________
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Re: Math: Number Theory
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