Number System is an all-time favourite with the CAT exam setters as well as the students. The topic is known for intriguing conceptual problems that test the best . CAT Number SYSTEM TEST 1(All 33). 1. Find the HCF of & 1. 2. 3. 4. 5. None of these. 2. Find the HCF of , 1. 2. 3. Download Number Systems Formulas for CAT PDF by Cracku. Number Systems is the most important topic in the quantitative section.

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CAT - Afternoon slot - Quantitative Aptitude - Number Systems - If the Download CAT Question Paper with answers and detailed solutions in PDF . CAT Study Material - Read concept of Number System and practice with Bonus: Download CAT Tips PDF that will help you boost your preparation. Abstract Algebra and Number Theory · Sequences and series of numbers and functions · Software Systems · CAT Group Discussion · CAT Personal Interview.

Divisible by 2 — If a number ends with 0,2,4,6,8 then the number is divisible by 2. Example — , , , All number ends with 4,6,8,0 so these numbers are divisible by 2. Example — ,, Example — Here last two digits 48 are divisible by 4, so is also divisible by 4. Example — , Here last 3 digits are divided by 8, hence the number is divisible by 8. Divisible by 10 — If a number ends with 0, then it is divisible by Example — , , Divisible by 12 — If a number is divisible by 3 and 4 both, then it will also be divisible by 12 as well. Example — is divisible by 3 and 4 both, so it will be divisible by 12 also. Divisible by 14 — If a number is divisible by 2 and 7 both, then it will also be divisible by 14 as well.

There are many prime sieves. The simple sieve of Eratosthenes BC , the sieve of Sundaram , the still faster but more complicated sieve of Atkin, , and various wheel sieves are most common.

A prime sieve works by creating a list of all integers up to a desired limit and progressively removing composite numbers which it directly generates until only primes are left. This is the most efficient way to obtain a large range of primes; however, to find individual primes, direct primality tests are more efficient.

Examples 1. Hence, the value of p is 2 or the power of 2. Option b 3. A, B, C, D and E are five prime numbers, not necessarily consecutive.

What is the value of A? As we know, 2 is only even prime number. So, the value of A should be 2.

The number of positive integers n in the range 12 n 40 such that the product n 1 n 2 n This is only possible if n is a prime number. The prime numbers in the range given are 13, 17, 19, 23, 29, 31, and There are 7 such numbers in all. Step 1: Take the approximate value of square root of N.

Step 2: Then divide the given number by all the prime numbers below the square root obtained. Step 3: If the number is divisible by any of these prime numbers then it is not a prime number else it is a prime number.

Example: Is a prime number? Solution: When we take the square root of it is approximate 15, so we consider Now we divide by all the prime numbers below Since is not divisible by 2, 3, 5, 7, 11 and So it is a prime number.

Divisible by 12 — If a number is divisible by 3 and 4 both, then it will also be divisible by 12 as well. Example — is divisible by 3 and 4 both, so it will be divisible by 12 also. Divisible by 14 — If a number is divisible by 2 and 7 both, then it will also be divisible by 14 as well.

Example — is divisible by 2 and 7 both, so it will be divisible by 14 also. Divisible by 15 — If a number is divisible by 3 and 5 both, then it will also be divisible by 15 as well.

Example — is divisible by 3 and 5 both, so it will be divisible by 15 also. Divisible by 16 — A number is divisible by 16, if the number formed by the last4 digits is divisible by Example - Last four digits are divisible by Divisible by 24 — If a number is divisible by 3 and 8 both, then it will also be divisible by 14 as well.

Example — is divisible by 3 and 8 both, so it will be divisible by 24 also. Divisible by 40 — If a number is divisible by 5 and 8 both, then it will also be divisible by 40 as well.

Example — is divisible by 5 and 8 both, so it will be divisible by 40 also.