Answer: 60 possible phone numbers.
Step-by-step explanation:
We want to find how may combinations of 4 numbers a, b, c, d have the product:
a*b*c*d = 336
we know that those numbers can be 7624.
The permutations of those 4 numbers can be:
4*3*2.
We can find other combinations of 4 numbers by the following.
Every number can be written as a product of prime numbers, here, for example, we have that 336 = 7*3*2^4
So we can play with the twos to get different combinations (with the 3 and the 7 we can not play because we have only one of those and we can not divide them into whole numbers)
Other 4 possible numbers are:
7*3*4*4
where i did:
7*6*2*4 = 7*(2*3)*2*4 = 7*3*4*4
where the number of permutations is:
4*3 (because one number repeats itself)
other combination is:
7*6*1*8
where we again have the number of permutations:
4*3*2
The total number of combinations is:
4*3*2 + 4*3*2 + 4*3 = 60
So we have 60 different possible numbers.
