Mathematics Plus: Maths tricks and short cuts for exams Bank PO, SSC, Clerical, Insurance, CSAT, others

MATHEMATICS FUNDAE FOR CLERICAL, BANK PO, SSC EXAMS AND OTHERS EXAMS

To find the number of factors of a given number, express the number as a product of powers of prime numbers.

Take the example of 576. 576 = 64*9 = 2⁶ x 3²

It is like 2⁰, 2¹, 2², 2³, 2⁴, 2⁵, 2⁶ X 3⁰, 3¹, 3²

To get No. Of factors what is there is that you take any thing from 2's power multiply by anthing from 3's power, that will divide your initial number because it has that many number of 2's and 3's . Right. So how many combination are possible ? On left are 7 and right are 3 so net will be 7 x 3 =21 factors.

In other words just remember

After finding that 2⁶ x 3² step, just do (6+1) x (2+1) = 7 x 3 =21 factors.

Note - If question ask you not to count 1 & 576 as factors, then subtract 2 from answer means 21-2=19. Otherwise don't subtract unnecessarily.

The sum of first n natural numbers = n (n+1)/2

Eg The sum of 1+2+3+……..+10+11+12 = ??

Here n = 12 so Sum = 12 ( 12+1 ) / 2

= 12 * 13 /2 = 6 * 13 = 78

The sum of squares of first n natural numbers is n (n+1)(2n+1)/6

Eg the sum of 1² + 2² + 3² + 4² + ………. +12² =??

= 12 (12+1) (2*12 + 1) /6

= 12*13*25 /6 = 650

The sum of first n even numbers= n (n+1)

Eg The sum of 2+4+6+8+10+…………. +40 = ??

Here n ≠40. N is the no of terms. So number of terms here is 20, the value of 20^th term is 40 indeed. So with n = 20

Sum = 20 (20+1) =20*21 =420

The sum of first n odd numbers= n²

Eg The sum of 1+3+5+7+9+11+…………..+21

Here n≠21. Here number of terms are 11 so n=11.

Sum = 11² = 121

To find the squares of numbers near numbers of which squares are known

For eg you might know squares of 20,30,40,.. Very easily.

To find square of 41 which is near to 40, Add 40+41 to 1600 =1681

To find 59² , which is near to 60, Subtract 60² - (60+59) =3600-119 = 3481

Add when the number is more and subtract when the number is less.

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