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<h2>Last digits of divisors</h2>
<h3>Problem 474</h3>
<div style="font-size:80%;color:#999;">Published on 01 June 2014 at 07:00 am [Server Time]</div>
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<p>
For a positive integer <var>n</var> and digits <var>d</var>, we define F(<var>n</var>, <var>d</var>) as the number of the divisors of <var>n</var> whose last digits equal <var>d</var>.<br>
For example, F(84, 4) = 3. Among the divisors of 84 (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84), three of them (4, 14, 84) have the last digit 4.
</p>
<p>
We can also verify that F(12!, 12) = 11 and F(50!, 123) = 17888.
</p>
<p>
Find F(10<sup>6</sup>!, 65432) modulo (10<sup>16</sup> + 61).
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<div style="text-align:center;" class="noprint">Answer not yet available</div>
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