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Zuckerman Number or Multiplication-Harshad Number or Multiplication-Niven Number

Zuckerman number or Multiplication-Harshad number or Multiplication-Niven number is any positive integer b that is divisible by its product of digits (POD) and all of its digits.

Zuckerman number cannot contain the digit 0. It is because if the digit 0 is present in the number, then multiplying it with other digits in the number gives the resultant 0, and no non-zero numbers are divisible by the digit 0.

As per the definition:

Zuckerman number b = number / product of digits

Below are some examples:

Number 24

Product of digits =  2 x 4 => 8

Here, number 24 is divisible by its product of digits 8, and the resultant is 3.

Apart from this, number 24 is divisible by all of its digits: 2 and 4.

Number 36

Product of digits = 3 x 6 => 18

Here, number 36 is divisible by its product of digits 18, and the resultant is 2.

Apart from this, number 36 is divisible by all of its digits: 3 and 6.

Number 115

Product of digits = 1 x 1 x 5 => 5

Here, number 115 is divisible by its product of digits 5, and the resultant is 23.

Apart from this, number 115 is divisible by all of its digits: 1, 1 and 5.

Number 175

Product of digits = 1 x 7 x 5 => 35

Here, number 175 is divisible by its product of digits 35, and the resultant is 5.

Apart from this, number 175 is divisible by all of its digits: 1, 7 and 5.

Number 224

Product of digits = 2 x 2 x 4 => 16

Here, number 224 is divisible by its product of digits 16, and the resultant is 14.

Apart from this, number 224 is divisible by all of its digits: 2, 2 and 4.

Hope you have understood the concept of Zuckerman number or Multiplication-Harshad number or Multiplication-Niven number. In case of any issue, kindly provide your valuable comments regarding the same.

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