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25=5x5 -- the same as [tex]5^2[/tex] 125=5x5x5 -- the same as [tex] 5^{3} [/tex]
As we can see there are 2 5s in the prime factors of 25 and 3 in the prime factors of 125. Therefore we pick the maximum number that is in both, which is 2, to get the HCF.
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