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Find the prime factors of the following numbers using the division method: i) 100 ii) 216 iii) 625 iv) 1000 v) 3900

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5 parts
i

2, 2, 5, 5\text{2, 2, 5, 5}

ii

2, 2, 2, 3, 3, 3\text{2, 2, 2, 3, 3, 3}

iii

5, 5, 5, 5\text{5, 5, 5, 5}

iv

2, 2, 2, 5, 5, 5\text{2, 2, 2, 5, 5, 5}

v

2, 2, 3, 5, 5, 13\text{2, 2, 3, 5, 5, 13}

Step-by-step solution

26 steps

Here are the prime factors for each number using the division method:

Part i· 4 steps

100

  1. Divide 100 by the smallest prime factor, 2.

    100÷2=50100 \div 2 = 50

  2. Divide 50 by 2.

    50÷2=2550 \div 2 = 25

  3. Divide 25 by the smallest prime factor, 5.

    25÷5=525 \div 5 = 5

  4. Divide 5 by 5.

    5÷5=15 \div 5 = 1

    The prime factors of 100 are 2, 2, 5, 5\boxed{\text{2, 2, 5, 5}}.

Part ii

2, 2, 2, 3, 3, 3\text{2, 2, 2, 3, 3, 3}

216

  1. Divide 216 by 2.

    216÷2=108216 \div 2 = 108

  2. Divide 108 by 2.

    108÷2=54108 \div 2 = 54

  3. Divide 54 by 2.

    54÷2=2754 \div 2 = 27

  4. Divide 27 by the smallest prime factor, 3.

    27÷3=927 \div 3 = 9

  5. Divide 9 by 3.

    9÷3=39 \div 3 = 3

  6. Divide 3 by 3.

    3÷3=13 \div 3 = 1

    The prime factors of 216 are 2, 2, 2, 3, 3, 3\boxed{\text{2, 2, 2, 3, 3, 3}}.

Part iii

5, 5, 5, 5\text{5, 5, 5, 5}

625

  1. Divide 625 by the smallest prime factor, 5.

    625÷5=125625 \div 5 = 125

  2. Divide 125 by 5.

    125÷5=25125 \div 5 = 25

  3. Divide 25 by 5.

    25÷5=525 \div 5 = 5

  4. Divide 5 by 5.

    5÷5=15 \div 5 = 1

    The prime factors of 625 are 5, 5, 5, 5\boxed{\text{5, 5, 5, 5}}.

Part iv

2, 2, 2, 5, 5, 5\text{2, 2, 2, 5, 5, 5}

1000

  1. Divide 1000 by 2.

    1000÷2=5001000 \div 2 = 500

  2. Divide 500 by 2.

    500÷2=250500 \div 2 = 250

  3. Divide 250 by 2.

    250÷2=125250 \div 2 = 125

  4. Divide 125 by 5.

    125÷5=25125 \div 5 = 25

  5. Divide 25 by 5.

    25÷5=525 \div 5 = 5

  6. Divide 5 by 5.

    5÷5=15 \div 5 = 1

    The prime factors of 1000 are 2, 2, 2, 5, 5, 5\boxed{\text{2, 2, 2, 5, 5, 5}}.

Part v

2, 2, 3, 5, 5, 13\text{2, 2, 3, 5, 5, 13}

3900

  1. Divide 3900 by 2.

    3900÷2=19503900 \div 2 = 1950

  2. Divide 1950 by 2.

    1950÷2=9751950 \div 2 = 975

  3. Divide 975 by 3.

    975÷3=325975 \div 3 = 325

  4. Divide 325 by 5.

    325÷5=65325 \div 5 = 65

  5. Divide 65 by 5.

    65÷5=1365 \div 5 = 13

  6. Divide 13 by 13.

    13÷13=113 \div 13 = 1

    The prime factors of 3900 are 2, 2, 3, 5, 5, 13\boxed{\text{2, 2, 3, 5, 5, 13}}.

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