### Brain Teasers

# A Pleasing Number

Which two closest together whole numbers that, when multiplied, produce the pleasant looking number: 1234567890 ?

### Answer

34,227 and 36,070.The only factors of 1234567890 are 2, 3, 3, 5, 3607 and 3803. Testing the various products of these factors reveals that 34,227 and 36,070 are the closest pair of numbers that produce 1234567890.

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## Comments

Those are just the prime factors. It would be

pretty hard to do this one without a factoring program

(like the Unix program "factor"), since the two largest

prime factors would be a lot of work to find by hand.

But given that factoring, I noted that the two large prime factors

were so close together that you really just wanted to find the closest

grouping of the small factors to multiply them. That gives 9 and 10 for the

best grouping of the small factors, and the answer follows.

pretty hard to do this one without a factoring program

(like the Unix program "factor"), since the two largest

prime factors would be a lot of work to find by hand.

But given that factoring, I noted that the two large prime factors

were so close together that you really just wanted to find the closest

grouping of the small factors to multiply them. That gives 9 and 10 for the

best grouping of the small factors, and the answer follows.

Yeah, once I had the prime factors I saw I could make 9 and 10 with the rest, so 10 * the smaller and 9 times the larger of the other two factors.

Once I got down to 13717421 and had tried the primes up to 100 I used the online factorization calculator at http://www.mathwarehouse.com/ arithmetic/numbers/prime-number/ prime-factorization-calculator.php to factor the rest.

Once I got down to 13717421 and had tried the primes up to 100 I used the online factorization calculator at http://www.mathwarehouse.com/ arithmetic/numbers/prime-number/ prime-factorization-calculator.php to factor the rest.

The (really simple) scip model that I used to solve this teaser can be found at

https://pastebin.com/QUMU2mGU

https://pastebin.com/QUMU2mGU

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