Question

Three students need to produce a prime factorization of 48. Donna states that the first factors in the tree should be 6 and 8. Larry states that the first factors in the tree should be 4 and 12. Trish states that the initial factors of 48 do not affect the prime factorization. Explain why Trish is correct.

Answer 1

f we start with 6 and 8, we can break 6 up into 2*3 and 8 into 2*2*2, thus getting a prime factorization of 2*2*2*2*3, or 2^4 *3.

If we begin with 4 and 12, 4 breaks into 2*2 and 12 into 2*2*3, so the prime factorization of 48 is still 2^4 *3.

The starting factors do not matter, since the answer comes out to be the same. There is exactly one correct answer- it doesn't matter how it's found.

Hope this helps! :)

Explanation:

Answer 2

Prime factorization means the product of the prime numbers that when multiplied, gives the original number.

Here the number is 48.

It does not matter from where we start, the answer will be same.

48 will have a prime factorization of 2 x 2 x 2 x 2 x 3

or
`2^(4) (3)`

So, if we break 6 and 8 or 4 and 12, the result will be same.