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I'd back a face-saver but it reduces dividends (7)

Ross

I believe the answer is:

divisor

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'it reduces dividends' is the definition.
The definition suggests a singular noun which matches the answer.

'i'd back a face-saver' is the wordplay.
'back' is a reversal indicator.
'a face-saver' becomes 'visor' (I can't explain this - if you can you should give a lot more credence to this answer).
'id' in reverse letter order is 'di'.
'di'+'visor'='DIVISOR'

'but' acts as a link.

Can you help me to learn more?

(Other definitions for divisor that I've seen before include "factor" , "Sort of number" , "B in A/B" , "Number under line" , "It will go in exactly" .)

I've seen this clue in The Globe and Mail.
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