How can you prove that the set of positive divisors of any (positive) integer n contains at least as many elements ending with 1 or 9 as elements ending with 3 or 7 ?

For example, the divisors of 63 are 1, 3, 7, 9, 21, 63 ; so 3 divisors end with 1 or 9 , and 3 divisors end with 3 or 7 .

For another example, the divisors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441 ; so 5 divisors end with 1 or 9 , and 4 divisors end with 3 or 7 .

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