Vamshi8411 wrote:

The positive integer 200 has how many factors?

A. 2

B. 10

C. 12

D. 15

E. 24

Can someone help me with a formula for such type of questions?

Finding the Number of Factors of an IntegerFirst make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\).

NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

BACK OT THE ORIGINAL QUESTION:

\(200=2^3*5^2\), so it has (3+1)(2+1)=12 different factors.

Answer: C.

For more check Number Theory chapter of Math Book:

math-number-theory-88376.htmlHope it helps.

as in factors of 200=(2)^3*(5)^2-->(3+1)(2+1)positive factors-->2*12(both positive and negative factors)=24?