How many factors of 360 are multiples of 6?

8Correct answerYour answer10Correct answerYour answer12Correct answerYour answer24Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$360 = 2^3 \times 3^2 \times 5$ .
A multiple of 6 needs at least one 2 and at least one 3.
Choices: power of 2 from 1 to 3 (3 ways), power of 3 from 1 to 2 (2 ways), power of 5 from 0 to 1 (2 ways).
Count = $3 \times 2 \times 2 = 12$ .

Worth noting

Equivalently, count the factors of $360 \div 6 = 60 = 2^2 \times 3 \times 5$ : $3 \times 2 \times 2 = 12$ . 24 is the total number of factors of 360.

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