Question

A certain set of numbers called Zuckerman numbers are Wlefined as those which are divisible by the product of their digits. The first few Zuckerman numbers are 1,2,3,4,5,6,7,8,9, and 11.

(a) Define a function (isZuckerman) that takes in a number, n, and returns whether the number would be defined as a Zuckerman number. If the value is not a Zuckerman number, return the closest Zuckerman number that is larger than the given number.
(b) A square number is one that can be written as n² for some integer n. Define a similar code as above (isSquare) that identifies square numbers.
(c) Can you find a two-digit Zuckerman number that is also a square number? (Consider using a for loop that will check both at the same time.)

Answer 1

To determine if a number is a Zuckerman number, check for divisibility by the product of its digits. If not divisible, find the closest Zuckerman number larger than the given number. For a two-digit Zuckerman number that is also a square number, use a for loop to check both conditions simultaneously.

Step-by-step explanation:

To determine whether a number is a Zuckerman number, we need to check if it is divisible by the product of its digits. If it is divisible, then it is a Zuckerman number. If it is not divisible, we need to find the closest Zuckerman number larger than the given number. Here is a Python code for the function:

def isZuckerman(n):
product = 1
for digit in str(n):
product *= int(digit)

if n % product == 0:
return True

closest_zuckerman = (n // product + 1) * product
return closest_zuckerman

To find a two-digit Zuckerman number that is also a square number, you can use a for loop to check both conditions simultaneously. Start the loop from 10 to 99 and check if the number is both a Zuckerman number and a square number.