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The number of applications that my new PC can execute at the same time is less than the number of applications that my old one can execute.

I revised the sentence above I created more simply as follows:

My new PC can execute a less number of applications at the same time than my old one.

Could you advise me on whether the usage "a less number of ... than" is correct.

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The use of "less" when referring to a number is common, but considered bad style by some. The word "fewer" is preferred by some.

Hence a simpler sentence could be

My new PC can execute fewer applications simultaneously than my old one.

You don't say "a less number" or "a fewer number".

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