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Q: How do you find prime factorization of 48 without using a factor tree or ladder digram?

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ladder method of 144

The prime factorization of 27 is 3 x 3 x 3.

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

5 x 5 = 25

*)1 7)7 3)21 2)42 The prime factorization of 42 is 2 x 3 x 7.

27 9,3 3,3,3

*)1 5)5 3)15 2)30 The prime factorization of 30 is 2 x 3 x 5.

The ladder method is used for converting metric measurements without a calculator.

3 x 3 x 5 x 7 = 315

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

There's no practical difference, it's just how you arrange the numbers.

34 has two prime factors: 2 and 17. It doesn't matter where you write them on the page.

84 42,2 21,2,2 7,3,2,2

The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! The greatest factor of any number is itself. So you do not need to use the division ladder or any other method!

A division ladder isn't necessary. Since 25 is a factor of 75, it is automatically the GCF of this problem.

No. if the floor is smooth you must have friction between the ladder and the floor, or the ladder would just slide away. Technically you could do without friction between wall and ladder, but even that can be helpful in preventing the ladder from going sideways.

you have to use a factor tree

No.

The prime factorization of 10 is 2 x 5. You need another number to find a GCF or LCM.

Don't bother. Since 25 is a factor of 75, it is automatically the GCF.

*)1 5)5 5)25 5)125 The prime factorization of 125 is 5 x 5 x 5.

either list factors, do factor trees, or division ladder

The GCF of consecutive numbers is 1.

The GCF is 3.

*)1 5)5 3)15 2)30 The prime factorization of 30 is 2 x 3 x 5.