The number of factors (excluding 1 and the expression itself) of the product of `a^(7)b^(4)c^(3)` def, where a, b, c, d, e, fare all prime numbers, is

Options

A. 1279
B. 1278
C. 1280
D. 1277

Explanation

To find the number of factors (excluding 1 and the expression itself) of the product \( a^{7}b^{4}c^{3}def \), where \( a, b, c, d, e, f \) are all prime numbers, we can follow these steps:

### Step 1: Identify the exponents of the prime factors
The expression can be written as:
\[ a^{7} \cdot b^{4} \cdot c^{3} \cdot d^{1} \cdot e^{1} \cdot f^{1} \]
Here, the exponents of the prime factors are:
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