Fun Fact(or)
What is the largest prime factor of 12345654321?
The answer is 37.
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2 solutions
Thanks! I thought of it first as 1 2 3 4 5 6 5 4 3 2 1 = ( 1 1 1 1 1 1 ) 2 . Now 1 1 1 1 1 1 = 1 1 1 0 0 0 + 1 1 1 = 1 0 0 1 × 1 1 1 . We have 1 1 1 = 3 × 3 7 and one might know the fun fact that 1 0 0 1 = 7 × 1 1 × 1 3 .
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Beautiful insight!
Same way Sir
Did the same!
Sir, Why you are replacing with (111111)^2 ?
L i t t l e C u r i o u s ! ! !
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I observe this fun fact: If you square the number x = 1 1 . . . 1 1 , with n ones in a row, where n < 1 0 , then x 2 = 1 2 3 . . . n . . . 3 2 1 : the digits go up to n and then back down again. In this problem, n = 6 .
Elegant indeed! Thank you
37^2 is one of the factor of the number the greatest prime factor is 37
This is interesting.
1 2 3 4 5 6 5 4 3 2 1 = 3 2 × 7 2 × 1 1 2 × 1 3 2 × 3 7 2
Therefore, the largest prime factor is 3 7