# Numbers with a shared property

The following numbers share same property.

What are the next two numbers with same shared property?

What are the previous two with the same shared property?

What is the largest three digit number with the same property?

What is the smallest two digit number with the same property?

One hundred thirty seven

Two hundred twenty five

Three hundred seventeen

Why did I write these numbers this way?

Why did I write these numbers this way?

The idea is that the product of the digits of the numbers are equal to the number of letters in the number itself:
137: $$1 \times 3 \times 7 = 21$$ "One hundred thirty seven" has 21 letters (ignoring spaces)
225: $$2 \times 2 \times 5 = 20$$ "Two hundred twenty five" has 20 letters
317: $$3 \times 1 \times 4 = 21$$ "Three hundred seventeen" has 21 letters

Now the side questions:

What are the next two numbers with same shared property?

522 and 613

What are the previous two with the same shared property?

91 and 42 (obviously 42, duh!)

What is the largest three digit number with the same property?

731

What is the smallest two digit number with the same property?

18, 25

Bonus:

You missed one between 137 and 225.... it's 219.

Explanation:

I cheated obviously..
I found this website (https://lingojam.com/NumbersToWords) that transforms numbers into words.
Then I wrote this js code in the browser console using their js function inEnglish which is the one called when you type something in the wensite

for (var i = 11; i< 1000; i++) {
var str = inEnglish(i).replace(/\s/g, '').replace('-', '').length;
var prod = 1;
var stringIndex = i.toString();
for (j = 0;j<stringIndex.length;j++) {
prod *= parseInt(stringIndex[j]);
}
if (prod === str) {
console.log(i);
}
} 

.

The output was all the numbers with this property from 11 to 999
18,25,42,91,137,219,225,317,522,613,731
I started from 11 because 10 results in a digit product of 0 and it makes no sense.

For Daniel Mathias... 1 digit numbers

4.... that's it.

• What about four? – Daniel Mathias Aug 12 '20 at 13:01
• @DanielMathias thanks for the heads up. Copy / paste malfunction. I edited the answer. I listed all the 2 and 3 digits numbers at the end of the answer anyway. – Marius Aug 12 '20 at 13:13
• But you have not included the single-digit number with the same property. – Daniel Mathias Aug 12 '20 at 16:33
• @DanielMathias. You are very picky. :). I will add the 1 digit numbers also. – Marius Aug 12 '20 at 17:29