Question

Total number of factors of a number is 24 and the sum of its 3 prime factors out of four, is 25. The product of all 4 prime factors of this number is 1365. Then such a greatest possible number can be

• A. 17745
• B. 28561
• C. 4095
• D. can't be determined

Answer 1

The correct option is A 17745

Since the Product of 4 prime factors = 1365
$=3\times 5\times 7\times 13$
and the sum of the 3 prime factors = 25 = (5 + 7 + 13)
Now, total number of factors of the required number N = 24
$=2^3\times 3\Rightarrow$ (1 + 1)(1 + 1)(1 + 1)(2 + 1)
Let N can be expressed as $N=3^p\times 5^q\times 7^r\times {13}^s$
Thus, in order to N will be greatest possible number in the
above expressed form, the power of the greatest prime
factors will be greater.
So $N=3\times 5\times 7\times {13}^2$
= 105 $\times$ 169 = 17745