Derek's phone number, $336$ - $7624,$ has the property that the three-digit prefix, $336,$ equals the product of the last four digits, $7 \times 6 \times 2 \times 4.$ how many seven-digit phone numbers beginning with $336$ have this property?

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.