Six of the factors of 1221 are palindromes: {1,3,11,33,111,1221} but two are not: {37,407}
(A) What number under one million has the most palindrome factors?
Some numbers have only palindromes as factors. Examples include 88: {1,2,4,8,11,22,44,88} and any palindromic prime
(B) Find the smallest number with at least as many palindrome factors as part (A) but having only palindrome factors.
(A) 792792 has 144 total factors of which 39 factors are palindromes
(B) There are 255 numbers 1 million or less such that all their factors are palindromes.
The one with the most palindrome-only factors is 48884 (18 factors).
Looking at numbers up to 100,000,000 which have only palindromes as factors, I found 3 such numbers with 18 (palindrome) factors: [48884, 448844, 2468642]. I found no numbers with more than 18 palindrome-only factors. Thus the goal of finding a number with 39 palindrome factor but no non-palindrome factors has not been achieved.
|
|
Posted by Larry
on 2022-03-15 07:26:00 |
Solution
