Factors - Atreya Roy


  • Content & PR team - MBAtious


    Author: Atreya Roy is pursuing his BTech From Kalyani Government Engineering College, Bengal.

    Factor of a number is a number smaller or equal to it which divides the number wholly. Hence factor of a number cannot exceed the number itself. Factors are always expressed as the product of primes present in that number.

    Example : Find the factors of 30

    Solution : 30 = 2 * 3 * 5

    In simple terms we can say that the factors of 30 = 1,2,3,5,6,10,15,30 : Total 8 factors.

    Let us look into a formula we can keep in mind so that we can calculate the number of factors fast.

    If the Number is represented in the form N = (a p)*(b q)*(c r)*(d s )…. Where a,b,c,d.. are the primes present in the number and p,q,r,s… are their respective exponents.

    So the number of factors in the number = (p+1)*(q+1)*(r+1)*(s+1)…….  And so on.

    Example :  Find the factors of 30

    Solution : 30 = 2^1 * 3^1 *5^1

    P=1

    Q=1

    R=1

    Hence the number of factors of 30 = (1+1)(1+1)(1+1) = 2*2*2 = 8 factors.

    Factors are of two types :

    1. Even factors : the factors which are divisible by 2
    2. Odd factors  : the factors which are not divisible by 2

    Example :

    Find the number of even factors in the number 3600

    Solution :

    Break 3600 into its prime factors. 3600 = 100*36 = 2^4*3^2*5^2

    Hence the total number of factors of 3600 = (4+1)*(2+1)*(2*1) = 45

    Out of these how many are even. For being even factors the factors must have atleast one 2 in them. Hence out of the four 2s present. Take out one. We are left with :

    2^3*3^2*5^2

    Hence, with these factors if we multiply the 2 we took out, we will get the total even factors.

    Total even factors = (3+1)*(2+1)*(2+1) = 4*3*3 = 36

    From this we can also find out the odd factors.

    Total Factors = Even Factors + Odd factors.

    Hence if the total number of factors = 45 and even factors are 36 then 45-36 = 9 odd factors are present in the number.

    Note : To find the number of odd factors present in a number we can also calculate them by removing all the 2s present in the number.

    Problem :

    We are given a number 64800. What are the total number of :

    1. Prime Factors
    2. Composite Factors
    3. Odd factors
    4. Even Factors

    Answer :

    Breaking 64800 into its factors, we get : 2^5 * 3^4 * 5^2 .

    1. Prime factors : 2,3,5 : hence 3 factors
    2. Total factors = (5+1)*(4+1)*(2+1) = 6*5*3 = 90
      Hence composite factors = total factors – prime factors-1 (since 1 is neither prime nor composite) = 90-3-1
    3. Odd Factors = factors in the number : 3^4 * 5^2 = (4+1)*(2+1 ) = 15
    4. Even Factors = total factors – odd factors = 90-15 = 75

     


Log in to reply
 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.