Question

The number 2 is chosen to begin a ladder diagram to find the prime factorization of 66. what other numbers could have been used to start the ladder diagram for 66? how does starting with a different number change the diagram

Answer 1

By changing the number for your prime factorization, you also have a different diagram.

Prime factorization for 66

66
/\
2*33
/\
3*11

Even if we change the prime factorization order, we still have the same numbers.

66 = 2 * 3 * 11

Answer 2

Explanation:

Given: The number 2 is chosen to begin a ladder diagram to find the prime factorization of 66.

Solution: Prime factorization of 66= 2×3×11.

Now, first consider the number 2 which is taken first to start the ladder, then the ladder diagram is as follows:

66

/\

2*33

/\

3*11

If we consider another number that is 3, the ladder diagram will change as:

66

/\

3*22

/\

2*11

Even if we change the prime factorization order, we still have the same numbers.