HOW TO GET THE NUMBER OF POSITIVE INTEGRAL DIVISORS OF A POSITIVE INTEGER?
Example 1: Ilan ang positive divisor ng 36?
By listing method:
1, 2, 3, 4, 6, 9, 12, 18, 36
Bale 9 yung divisors diba? Pero kelangan bang ilista lahat yan? Paano kung thousands yung given? Ang hirap nun. Basta alam mo lang yung PRIME FACTORIZATION, madali nalang sayo to.
SOLUTION:
Kunin ang prime factorization ng 36
36 = 2 x 2 x 3 x 3 = 2^2 x 3^2
Kunin mo yung exponent ng kada prime factor. So, kunin mo yung 2 at yung isa pang 2.
Always add 1 to each exponent. Bale 2+1 = 3, tsaka yung isa pa, 2+1 = 3
Bale multiply mo yung 3 tsaka 3.
3 x 3 = 9 :)
Example 2: Ilan ang positive divisor ng 360?
By listing method:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
So 24 yung divisors. Gawin natin yung simple method:
SOLUTION:
360 = 2 x 2 x 2 x 3 x 3 x 5 = 2^3 x 3^2 x 5
Kunin exponent nila.
Exponent ng 2 ay 3
Exponent ng 3 ay 2
Exponent ng 5 ay 1
Add 1 sa lahat ng exponent then multiply:
(3+1)(2+1)(1+1) = (4)(3)(2) = 24 :)
#MMBLTutorial
-shinnichi
