To figure this out you should first express the numbers as the product of their prime factors:
27 = 3x3x3
45 = 3x3x5
The next step is to identify any common prime factors. Both numbers have two 3s as prime factors. Multiply these together and you get:
3x3 = 9
Thus 9 is the HCF of 27 and 45.
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To find this, you need to split the numbers into their prime factors:
45 = 3x3x5
27 = 3x3x3
The next step is to identify any common prime factors. In this case, both numbers have two 3s as prime factors. Multiply these together and you get 9. Thus the HCF of 45 and 27 is 9.