Skip to main content

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.

Labels:

Comments

Post a Comment

Popular posts from this blog

The Number 1.6: Base of Fibonacci Sequence and the Golden Ratio

This post is about the number 1.6 that forms the base of the mathematical concepts Fibonacci sequence and the Golden ratio. For better understanding of this amazing number 1.6, it is important to know about Fibonacci sequence and the Golden ratio. Golden Ratio The  Golden ratio is the ratio of a line segment cut into two pieces of distinct lengths such that the ratio of the longer segment to the shorter segment is equal to the whole segment to that of the longer segment. It is denoted by the symbol Phi [ø]. Suppose there is a line segment AB, and C is any point that divides the line segment AB into two pieces of distinct lengths such that AC is greater than CB. Then, as per the definition, [ø] = AC/CB = AB/AC. The value of the Golden ratio [ø] is 1.6 1803398875 . As you can see, the value of the Golden ratio starts with the number 1.6. For more information on the Golden ratio, see https://theamazingconcepts.blogspot.com/2021/07/the-golden-ratio-key-to-amazing-design....
Post a Comment
Read more

Universe Secret Code 369 Theory

When it comes to the origin of the universe secret code 369 theory, one name associated with this amazing concept is ‘Nikola Tesla’. Nikola Tesla [10 July 1856 – 07 January 1943] was not only a great inventor / scientist, but also the greatest mind of all the time. He has done a plenty of research throughout his life, and highly recognized for his contributions towards the following : High Voltage, High Frequency Power Experiments Alternating Current (AC) Electricity Supply System Apart from the above-mentioned contributions, he has given ‘Universe Secret Code 369 Theory’ and has called the number 369 – the key to the universe. Now the question that will come to the curious minds is that why Nikola Tesla has called this number the key to the universe. The answer to this question is described in this post. Let start with a specific pattern as shown below: 1 1 + 1 => 2 2 + 2 => 4 4 + 4 => 8 8 + 8 => 16; 1 + 6 => 7 16 + 16 => 32; 3 + 2 => 5 >>>>>>...
Post a Comment
Read more

Nivenmorphic Number or Harshadmorphic Number

A Nivenmorphic number or Harshadmorphic number is a positive integer whose sum of digits is the last digits of the number i.e. the sum of the digits terminates the number. The Concept Step 1:  Take any positive integer. Step 2:  Calculate the sum of the digits of the number. Step 3:  If the sum of the digits is the last digits of the number i.e. the sum of the digits terminates the number, then the number is a Nivenmorphic number or Harshadmorphic number, else not. For Example Number: 16218 Sum of the digits of the number: [1 + 6 + 2 + 1 + 8] => 18 Here, the sum of the digits 18 is the last digits of the number i.e.  the sum of the digits terminates the number.  Hence, the number 16218 is a Nivenmorphic number or Harshadmorphic number. Hope you have understood this amazing concept of Nivenmorphic number or Harshadmorphic number. You can try yourself using any other positive integer. In case of any issue, kindly pro...
Post a Comment
Read more