Break down the following numbers by their prime factors: 6, 72, 108, 30, 60, 150.

Here are the breakdowns for each number:

1. Break down the number by multiplying 2s and 3s.

a)

Step 1: Divide 6 by 2.

$$6 = 2 \times 3$$

The number 6 is broken down into factors of 2 and 3.

b)

Step 1: Divide 72 by 2.

$$72 = 2 \times 36$$

Step 2: Divide 36 by 2.

$$72 = 2 \times 2 \times 18$$

Step 3: Divide 18 by 2.

$$72 = 2 \times 2 \times 2 \times 9$$

Step 4: Break down 9 into factors of 3.

$$72 = 2 \times 2 \times 2 \times 3 \times 3$$

The number 72 is broken down into factors of 2s and 3s.

c)

Step 1: Divide 108 by 2.

$$108 = 2 \times 54$$

Step 2: Divide 54 by 2.

$$108 = 2 \times 2 \times 27$$

Step 3: Break down 27 into factors of 3.

$$108 = 2 \times 2 \times 3 \times 9$$

Step 4: Break down 9 into factors of 3.

$$108 = 2 \times 2 \times 3 \times 3 \times 3$$

The number 108 is broken down into factors of 2s and 3s.

2. Break down the number by multiplying 2s or 3s or 5s or a combination.

a)

Step 1: Divide 30 by 2.

$$30 = 2 \times 15$$

Step 2: Break down 15 into factors of 3 and 5.

$$30 = 2 \times 3 \times 5$$

The number 30 is broken down into factors of 2, 3, and 5.

b)

Step 1: Divide 60 by 2.

$$60 = 2 \times 30$$

Step 2: Divide 30 by 2.

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