Question

1.) Find all the factors of 54.

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