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Factor it (Posted on 2019-03-19) Difficulty: 3 of 5
What is the largest prime factor of 8888888899999999?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution | Comment 1 of 3
Start by factoring  out the easy bits:
8888888899999999 = 11111111*800000009

11111111=1111*10001=11*101*73*137

The factoring program on my calculator can easily handle 5-digit numbers like 10001, but not 9-digit numbers.  If I let it run long enough I can easily see 80000009 is either prime or has prime factors above 10001.

Turning to Wolfram|Alpha I can get the last factors (it feels like cheating) and 800000009=15299*52291.

So the largest prime factor is 52291.

And my calculator just found it as I was typing!

  Posted by Jer on 2019-03-19 10:06:22
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