The organism with no nucleus that divides into two identical organisms is a bacterium.

Here's why:

* No nucleus: Bacteria are prokaryotes, meaning they lack a membrane-bound nucleus and other membrane-bound organelles. Their genetic material (DNA) is located in a region called the nucleoid, which is not enclosed by a membrane.

* Binary fission: Bacteria reproduce asexually through a process called binary fission. This involves the following steps:

1. The bacterium's DNA replicates.

2. The cell grows in size.

3. The cell membrane pinches inward, dividing the cell into two identical daughter cells.

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