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

Sample Response: A prime factorization is the product of the prime numbers that multiply to give the original number. 48 will have a prime factorization of 2(2)(2)(2)(3), or 24(3), regardless of the initial factors.

Answer 2

If 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! :)