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Find the prime factors for the following numbers: a) 27 b) 40 c) 50 d) 75 e) 90

Mathematics

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Answers

5 parts
a

3, 3, 3\text{3, 3, 3}

b

2, 2, 2, 5\text{2, 2, 2, 5}

c

2, 5, 5\text{2, 5, 5}

d

3, 5, 5\text{3, 5, 5}

e

2, 3, 3, 5\text{2, 3, 3, 5}

Step-by-step solution

12 steps

Here are the prime factors for each number using the factor tree method:

Part a· 2 steps

27

  1. Start with 27.

    27=3×927 = 3 \times 9
  2. Break down 9.

    9=3×39 = 3 \times 3

    The prime factors are the numbers at the end of the branches.
    The prime factors of 27 are 3, 3, 3\boxed{\text{3, 3, 3}}.

Part b

2, 2, 2, 5\text{2, 2, 2, 5}

40

  1. Start with 40.

    40=2×2040 = 2 \times 20
  2. Break down 20.

    20=2×1020 = 2 \times 10
  3. Break down 10.

    10=2×510 = 2 \times 5

    The prime factors are the numbers at the end of the branches.
    The prime factors of 40 are 2, 2, 2, 5\boxed{\text{2, 2, 2, 5}}.

Part c

2, 5, 5\text{2, 5, 5}

50

  1. Start with 50.

    50=2×2550 = 2 \times 25
  2. Break down 25.

    25=5×525 = 5 \times 5

    The prime factors are the numbers at the end of the branches.
    The prime factors of 50 are 2, 5, 5\boxed{\text{2, 5, 5}}.

Part d

3, 5, 5\text{3, 5, 5}

75

  1. Start with 75.

    75=3×2575 = 3 \times 25
  2. Break down 25.

    25=5×525 = 5 \times 5

    The prime factors are the numbers at the end of the branches.
    The prime factors of 75 are 3, 5, 5\boxed{\text{3, 5, 5}}.

Part e

2, 3, 3, 5\text{2, 3, 3, 5}

90

  1. Start with 90.

    90=2×4590 = 2 \times 45
  2. Break down 45.

    45=3×1545 = 3 \times 15
  3. Break down 15.

    15=3×515 = 3 \times 5

    The prime factors are the numbers at the end of the branches.
    The prime factors of 90 are 2, 3, 3, 5\boxed{\text{2, 3, 3, 5}}.

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