Question

If $2200=2^a\times 5^b\times {11}^c\times 3^d,$ then $a+b-c+d=$ .

• A. 4
• B. 2
• C. 5
• D. 3

Answer 1

The correct option is A 4

Using fundamental theorem of arithmetic, every composite number can be uniquely expressed as the product of its primes $2200=2^3\times 5^2\times 11.$
Thus, on comparison with $2^a\times 5^b\times {11}^c\times 3^d,$ we get $a=3,b=2,c=1$ and $d=0.$
Thus, $a+b-c+d=3+2-1+0=4.$