Cat Coaching centre in hyderabad

1. CAT Coaching Centre in Hyderabad Title:CAT Coaching Centre in Hyderabad. Keyword: CAT Coaching Centre in Hyderabad | CAT Coaching Centre Hyderabad | CAT Coaching Centre | CAT Coaching | CAT Training Centre in Hyderabad | CAT Training Centre. Description: As you decide to start your preparation for CAT 2018, you keep fishing around for proper exam syllabus description! Euler’s Theorem:Euler’s theorem is a generalization of Fermat’s little theorem and is very helpful in finding remainders. CAT Coaching Centre in Hyderabad The remainder questions in Number System seem to be very difficult and scary but they can be simplified using Euler’s theorem. One of the sub-concept that you need to know in numbers system is the concept of Co- Primes. Co-Primes: Two or more numbers are said to be co-primes if their HCF is 1.Any two consecutive natural numbers are always co-primes. Euler’s Totient: Euler’s totient of a number gives us the number of co-primes less than that number.It is denoted by ϕ(n) where ‘ϕ’ is a Greek letter pronounced as “Phi”. If Prime Factorization of N :ap*bq *cr*ds Then ϕ(N) = N*(1-1/a)*(1-1/b)*(1-1c)*(1-1/d). where ϕ(N) is the number of Co-primes less than N. Φ(24) =24(1-1/2)(1-1/3)=8. Therefor, 24 has 8 numbers less than 24 that are co-primes to it. Φ(100) = 100(1-1/2)(1-1/5)=40 Here 100 has 40 numbers less than 100 that are co-primes to it.

2. Φ(150) = 150(1-1/5)(1-1/2)(1-1/3) = 40. And 150 has 40 numbers less than 150 that are co-primes to it. Application of Euler’s Theorem: 1. Whatis the remainder when 257256 divided by 24? We will have to note that 257 and 24 are co-primes. Here we divide base with 24 and power with ϕ(24).CAT Training Centre . 257 when divided by 24 gives a remainder of 17 and 256 when divided by ϕ(24) gives a remainder of 0 R{257256/24} = R{170}=1 2. Find the last two digits of 203202? We know that the last 2 digits of a number are exactly the same as the remainder when the number is divided by 100.So, we are supposed to find the remainder of 203202 when divided by 100. 203 when divided by 100 gives a remainder of 3. 202 when divided by 40 gives a remainder of 2. R{203202/100} = R{32/100}=09. 3. Find the remainder when ??????divided by 11? Here we divide 53 with 11,52 with 10 and 51 with 4. 53 divided by 11 will gives us a negative remainder of -2. 52 when divided by 10 gives a remainder 2. 51 when divided by 4 gives a remainder 3. R{ 535251/11} =R{((−2)23/11}= R{28/11}=3.