First, find the prime factorization. Use a factor tree.
189
63,3
21,3,3
7,3,3,3
All the other factors will be combinations of these. There are eight altogether.
You know that 1, 3 and 7 are factors. The rules of divisibility tells you that 9 is as well. Dividing them into 189 gives you the rest.
1, 3, 7, 9, 21, 27, 63, 189
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To find the largest perfect cube factor of 189, we first need to factor it into its prime components. The prime factorization of 189 is (3^3 \times 7^1). The largest perfect cube that can be formed from these factors is (3^3), which equals 27. Therefore, the largest perfect cube factor of 189 is 27.
Since 27 is a factor of 189, it is automatically the GCF.
The GCF of 66 and 189 is 3.
The factors of 189 are 1 3 7 9 21 27 63 189 So the largest factor is 189. However, 189 is not a proper factor, even though it is a factor. The largest proper factor is 63. Now 63 is not prime, since is is clearly divisible by 3. The largest prime factor is 7
The GCF is 27.