ladder method
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prime factors
The prime factorization of 27 is 3 x 3 x 3.
As a product of its prime factors: 3*5*31 = 465
To find the prime factorization of 126 using the ladder method, we start by dividing 126 by the smallest prime number, which is 2. This gives us 63. Then, we divide 63 by 3, which gives us 21. Continuing this process, we find that 21 can be divided by 3 again to get 7. Therefore, the prime factorization of 126 is 2 x 3 x 3 x 7, or 2 x 3^2 x 7.
As a product of its prime factors in exponents: 22*3*7 = 84