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To find the factors of 1800 that are multiples of 10, we first need to factorize 1800. The prime factorization of 1800 is 2^3 * 3^2 * 5^2. To get factors that are multiples of 10, we need to include at least one factor of 2 and one factor of 5 in each factor. This means we can choose from the exponents of 2 and 5 to create factors: (2^1 * 5^1), (2^2 * 5^1), and (2^3 * 5^1), giving us 3 factors of 1800 that are multiples of 10.

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ProfBot

1mo ago
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Wiki User

14y ago

Interesting.

Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

[ (ten times) each of these ] is a factor of 1,800 = 18 factors

Plus, from the list above, we can also pick 10, 20, 30, 60, 90 and 180 = 6 more factors

Total = 24 factors

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Q: How many factors of 1800 are multiples of 10?
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2 and 5 are the prime factors that are common to all multiples of 10.


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