MHB Whatzit? Number Fun - 144 / (1 + 4 + 4) = 1*4*4

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The discussion centers around a mathematical relationship where a three-digit number can be expressed as the product of its digits multiplied by their sum. The example given is 144, which satisfies the equation 144 / (1 + 4 + 4) = 1 * 4 * 4. A Python code snippet is shared to identify such numbers, revealing that 144 and 135 are the only three-digit numbers that meet this criterion. Attempts to find similar relationships in two-digit and four-digit numbers yielded no results. The conversation highlights the effectiveness of the code in identifying these specific numbers, emphasizing the uniqueness of the findings.
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144 / (1 + 4 + 4) = 1*4*4

There is another 3digit number that works similarly: whatzit?
 
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Simple python code found it:
[sp]
Code:
[FONT=Courier New]
for i in range(1,9):
    for j in range(1,9):
        for k in range(1,9):
            if 100*i + 10*j + k == i*j*k*(i + j + k):
                print(i,j,k)
It found 144 and 135. Those are the only ones!
[/sp]
 
Yepper!
Your code is exactly like mine; I use UBasic.

Tried with 2digit and 4digit numbers: none.
 
Ackbach said:
Simple python code found it:
[sp]
Code:
[FONT=Courier New]
for i in range(1,9):
    for j in range(1,9):
        for k in range(1,9):
            if 100*i + 10*j + k == i*j*k*(i + j + k):
                print(i,j,k)
It found 144 and 135. Those are the only ones!
[/sp]

Erm... range(1,9) = (1,...,8) in python.
It's a good thing there are no numbers with a 9 in it!
 
I like Serena said:
Erm... range(1,9) = (1,...,8) in python.
It's a good thing there are no numbers with a 9 in it!

Oops! How embarrassing.
 
Go stand in the corner for 13.5 minutes :)
 
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