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Last digits of divisors

Problem 474 Published on Sunday, 1st June 2014, 07:00 am; Solved by 292;
Difficulty rating: 50%

For a positive integer n and digits d, we define F(n, d) as the number of the divisors of n whose last digits equal d.
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.

We can also verify that F(12!, 12) = 11 and F(50!, 123) = 17888.

Find F(106!, 65432) modulo (1016 + 61).