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You can do it in your head. Cutting something in half is the same as dividing by a factor of 2. Cut 48 in half. Cut 24 in half. Cut 12 in half. Cut 6 in half.

2 x 2 x 2 x 2 x 3 = 48

Q: How do you find the prime factorization 48 without using factor tree or ladder diagram?

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As a product of its prime factors: 2*3*3*7 = 126

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It's not really. The process is essentially the same. It's just a matter of where on the page you write the numbers.