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www.mahendraguru.com (Maths) KEY POINTS: Only ‘2’ is an even prime number. There is only one set of three prime numbers with a gap of 2 between two prime numbers and that set is 3, 5 and 7. Lowest composite number is 4. 1st odd composite number is 9. There are total 25 prime numbers up to 100. There are total 46 prime numbers up to 200. Sum of 1 to 50 prime numbers = 328. Sum of 1 to 100 prime numbers = 1060. BASIC TOOLS: The number of zeroes at the end of the product of numbers equals the number of combination of the product (2 x5) in the given product. i.e. (2n x 5n) = (2x5)n = n (where n = number of zeroes) Number of zeroes--- n! Number of zero = + ------- (where numerator ) Number of divisors or factors----If N is any number which can be factorized like N = Pa X Qb X Rc ----- (where P,Q and R are prime number). Number of divisors = (a +1) (b + 1) (c + 1) --------BASIC FORMULE: 1. 2. 3. 4. 5. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2 (12 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6 (13 + 23 + 33 + ..... + n3) = {n(n + 1)/ 2}2 Sum of first n odd numbers = n2 Sum of first n even numbers = n (n + 1) Date of Release -23-Jan-16 SUBJECT- MATHS www.mahendraguru.com