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Splitting large text file into smaller text files by line numbers using Python

I have a text file say really_big_file.txt that contains:

line 1
line 2
line 3
line 4
...
line 99999
line 100000

I would like to write a Python script that divides really_big_file.txt into smaller files with 300 lines each. For example, small_file_300.txt to have lines 1-300, small_file_600 to have lines 301-600, and so on until there are enough small files made to contain all the lines from the big file.

I would appreciate any suggestions on the easiest way to accomplish this using Python

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lines_per_file = 300
smallfile = None
with open('really_big_file.txt') as bigfile:
    for lineno, line in enumerate(bigfile):
        if lineno % lines_per_file == 0:
            if smallfile:
                smallfile.close()
            small_filename = 'small_file_{}.txt'.format(lineno + lines_per_file)
            smallfile = open(small_filename, "w")
        smallfile.write(line)
    if smallfile:
        smallfile.close()

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