It was shown in this paper (see formula (2) there) that any normal random variable (r.v.) $Z$ is multiplicatively infinitely divisible; that is, for each natural $k$ there exist iid r.v.'s $W_1,\dots,W_k$ such that $Z$ equals $W_1\cdots W_k$ in distribution; the distribution of $W_1$ is explicitly described.
Iosif Pinelis
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