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ExpertsGlobal5
If a, b, c, d, e, and f represent different prime numbers each, which of the following may represent the value of 16! ?

A. a^15 x b^6 x c^3 x d^2 x e^2 x f
B. a^15 x b^5 x c^3 x d^2 x e x f^2
C. a^15 x b^6 x c^3 x d^2 x e x f
D. a^8 x b^5 x c^3 x d^2 x e x f
E. a^8 x b^5 x c^2 x d^2 x e x f


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The value 16! includes the following prime numbers: 2,3,5,7,11,13.

So, each of the following represent the variables a,b,c,d,e,f.

Prime numbers 13 and 11 occurs only once .

7 occurs twice.

Among the options C, D, E matches.

If we divide 16! Successively by 2, we get 8+4+2+1 = 15.

The power of a is 15.

Amongst the three possible answer choices - Option C matches our result.

C. a^15 x b^6 x c^3 x d^2 x e x f
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16! has eight multiples of 2, four multiples of 4, two multiples of 8, and one multiple of 16 (8+4+2+1=15).
This quickly eliminates options D and E.

Now the remaining primes are 3,5,7,11,13

11 and 13 only come once so 2 prime numbers must have power 1
This also eliminates options A and B.

So, C is the answer.
You can also check by prime factorization of 16! but this will take time time.
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ExpertsGlobal5
If a, b, c, d, e, and f represent different prime numbers each, which of the following may represent the value of 16! ?

A. a^15 x b^6 x c^3 x d^2 x e^2 x f
B. a^15 x b^5 x c^3 x d^2 x e x f^2
C. a^15 x b^6 x c^3 x d^2 x e x f
D. a^8 x b^5 x c^3 x d^2 x e x f
E. a^8 x b^5 x c^2 x d^2 x e x f

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