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Find all the factors of 18. State which of these factors are even numbers. State which of these factors are prime numbers. Write the first three multiples of 18.

Mathematics

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Answers

4 parts
a

1, 2, 3, 6, 9, 18\text{1, 2, 3, 6, 9, 18}

b

2, 6, 18\text{2, 6, 18}

c

2, 3\text{2, 3}

d

18, 36, 54\text{18, 36, 54}

Step-by-step solution

4 steps

Here are the solutions for Example 1.1:

Part a· 1 step

Find all the factors of 18.

  1. Identify all pairs of integers that multiply to 18.

    1×18=181 \times 18 = 18 2×9=182 \times 9 = 18 3×6=183 \times 6 = 18

    The factors are the numbers in these pairs.
    The factors of 18 are 1, 2, 3, 6, 9, 18\boxed{\text{1, 2, 3, 6, 9, 18}}.

Part b

2, 6, 18\text{2, 6, 18}

State which of these factors are even numbers.

  1. From the factors of 18 (1, 2, 3, 6, 9, 18), identify numbers that are divisible by 2.

    The even factors are 2, 6, 18\boxed{\text{2, 6, 18}}.

Part c

2, 3\text{2, 3}

State which of these factors are prime numbers.

  1. From the factors of 18 (1, 2, 3, 6, 9, 18), identify numbers greater than 1 that have only two factors

    1 and themselves.

    • 1 is not prime.
    • 2 is prime (factors: 1, 2).
    • 3 is prime (factors: 1, 3).
    • 6 is not prime (factors: 1, 2, 3, 6).
    • 9 is not prime (factors: 1, 3, 9).
    • 18 is not prime (factors: 1, 2, 3, 6, 9, 18). The prime factors are 2, 3\boxed{\text{2, 3}}.

Part d

18, 36, 54\text{18, 36, 54}

Write the first three multiples of 18.

  1. Multiply 18 by the first three positive integers (1, 2, 3).

    18×1=1818 \times 1 = 18 18×2=3618 \times 2 = 36 18×3=5418 \times 3 = 54

    The first three multiples of 18 are 18, 36, 54\boxed{\text{18, 36, 54}}.

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