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Essay on Number System

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he number theory or number systems happens to be the back bone for CAT preparation. Number systems not only form the basis of most calculations and other systems in mathematics, but also it forms a major percentage of the CAT quantitative section. The reason for that is the ability of examiner to formulate tough conceptual questions and puzzles from this section. In number systems there are hundreds of concepts and variations, along with various logics attached to them, which makes this seemingly easy looking topic most complex in preparation for the CAT examination. The students while going through these topics should be careful in capturing the concept correctly, as it’s not the speed but the concept that will solve the question here. …show more content…

Example: 2, 23,5,7,11,13 etc. Here are some properties of prime numbers:

• The only even prime number is 2
• 1 is neither a prime nor a composite number
• If p is a prime number then for any whole number a, ap – a is divisible by p.
• 2,3,5,7,11,13,17,19,23,29 are first ten prime numbers (should be remembered)
• Two numbers are supposed to be co-prime of their HCF is 1, e.g. 3 & 5, 14 & 29 etc.
• A number is divisible by ab only when that number is divisible by each one of a and b, where a and b are co prime.
• To find a prime number, check the rough square root of the given number and divide the number by all the prime number lower than the estimated square root
• All prime numbers can be expressed in the form 6n-1 or 6n+1, but all numbers that can be expressed in this form are not prime

Example: If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is: (CAT 2003)

(a) 1 (b) 2
(c) 3 (d) more than 3

Ans. (a) a, a + 2, a + 4 are prime numbers. The number fits is 1, 3, 5 and 3, 5, 7 but post this nothing will fit. Now 1, 3, 5 are not prime numbers as 1 is not prime number.
So, only one possibility is there 3, 5, 7 for a = 3.
Prime Factors: The composite numbers express in factors, wherein all the factors are prime. To get prime factors we divide number by prime numbers till the remainder is a prime number. All composite numbers can be

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