Question

1.) Find all the factors of 54.
2.) Find all the prime factorization of 54, and then write it using exponents.
3.) Find all the factors of 60.
4.) Find the prime factorization of 60, and then write it using exponents.
5.) Chanasia has 30 beads. She wants to put them in boxes. So that each box will contain the same whole numbers of beads. Use factors to list all the different ways she can put the beads into boxes

Please explain how you got your answers :)

Answer 1

QUESTION 1.

The factors of 54  are all natural numbers that can divide 54 exactly.

The factors of 54 are: {1,2,3,6,9,18,27,54}

QUESTION 2

The prime factors of 54 are factors of 54 that are prime numbers.

The prime factors of 54 are {2,3}.

Product of prime factors of 54 is $2\times 3^3$

QUESTION 3

All the factors of 60 are all positive integers that divide exactly into 60.

The factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}

QUESTION 4

The prime factors of 60 are factors of 60 that are prime numbers.

The prime factors of 60 are {2,3,5}

The prime factorization of 60 is $2^2\times 3\times 5$.

QUESTION 5

The factors of 30 are {1,2,3,5,6,10,15,30}

The different ways she can put the beads into the boxes are

$1\times 30$,

All 30 beads into one box or 1 bead in 30 boxes.

$2\times 15$,

2 beads each into 15 boxes or 15 beads each into 2 boxes

$3\times 10$,

3 beads each into 10 boxes or 10 beads each into 3 boxes

$5\times 6$,

6 beads each into 5 boxes or 5 beads each into 6 boxes