Yes, there is a standard formula.
If you decompose a number N to its prime factors such that
N = a^i * b^j * c*k..., where a, b and c are prime numbers.
and i, j , k are +ve integers, then the total number of factors is
(i+1) * (j+1) *(k+1).
U are already wondering why we add 1 to the powers. This +1 accounts for 0th power of the corr prime number. ie a^0 =1 is also a factor of N.
in a^4b^3 in this problem the * is implicit.. Pls read it as
a^4 *b^3
Also, with B it's saying that there are only 2 prime factors 5 and 7. To me, that means that there are no other factors since every other number can be simplified to a prime factor (ex, 6, 4, 8, 9) which is why I chose B. Is this correct?
From B we only know the prime factors. From that we cannot predict all the factors. ie we need to know the powers of these prime factors to find the number of prime factors.
Put this another way: From B, we know that 5 and 7 are prime factors.
But we dont know if N = 5*7 or N=5^a * 7^b.
So this is insufficient.
HT Helps
Ht Helps
