Question

Little Shino loves maths. Today her teacher gave her two integers. Shino is now wondering how many integers can divide both the numbers. She is busy with her assignments. Help her to solve the problem.

Answer 1

Hey Little Shino !

Assuming that Shino only wants Positive Divisors ^^"

Say, Shino got two Integers " a " , " b "

Find the GCD of ( a , b )

Now, Shino has to Rewrite all the Divisors in the canonical form :

$gcd(a,b) = p_{1}^{ \alpha _{1} } .p_{2}^{ \alpha _{2} } .p_{3}^{ \alpha _{3} } ...p_{n}^{ \alpha _{n} }$

+_+ Shino can find the number of Divisors of the both the Numbers as :

$(1 + \alpha _{1})(1 + \alpha _{2})...(1 + \alpha _{n})$
Now,

If by any chance, Little Shino also wants the number of Negative Divisors Combined, The Total Number of Divisors are :

$2(1 + \alpha _{1})(1 + \alpha _{2})(1 + \alpha _{3})...(1 + \alpha _{n})$

Goodluck impressing your teacher Shino ^^

Answer 2

Concept: The numbers that can divide perfectly without leaving a leftover are those that can be used as factors of two or more numbers. The term "factor" refers to a number that can divide another number perfectly, leaving zero as the undivided result. We see that some factors are the same or frequent when we compare the factors of two or more integers. These elements are referred to as common factors.

Given: Two numbers are given to Shino.

Find:  To find all the common divisors of the chosen two numbers.

Solution: The exact divisors of a number are known as its factors.  Let's examine the procedures for identifying the common components.

Step 1.  List each component of the supplied integers in a separate row.

Step 2: Examine the factors that are shared by the supplied numbers, and then list each one in a distinct row.

Hence, we solve the problem using the above-given algorithm of two steps.

#SPJ3