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This book "Deep Learning and Convolutional Neural Networks for Medical Image Computing" uses an expression "a factor of K-fold".

As we learned about the current state of research on deep learning, I was surprised to find that other investigators had used convolutional neural networks, one type of deep learning, in the past [22, 23]. But there seemed to be something different about the most recent crop of deep learning algorithms. They routinely used GPU processing to accelerate training by as much as a factor of 40-fold. They also used multiple convolution layers and multiple data reduction layers.

It seems that "a factor of 40-fold" means "×40 faster than before".

Is "a factor of K-fold" a idiomatic saying to express this meaning?

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It's okay, but a bit redundant.

It is idiomatic to say "It increased 40-fold", or "It increased by a factor of 40". These mean the same, the amount was multiplied by 40. Saying "increased by a factor of 40-fold" mixes these two expressions, which isn't right, but we understand what is meant.

If this is your writing I would suggest editing to tighten the phrasing. If it is someone else then you should be able to understand it.

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