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All the factors of 200 and all the factors of 300 are factors of 600. True or false and explain.

All the factors of 200 and all the factors of 300 are factors of 600. True or false-example-1
User Jbcurtin
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2 Answers

5 votes

Answer:

true because 200 and 300 are factors of 600

Explanation:

User Jomido
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7 votes

Answer:

I don't think so

Explanation:

600 is a composite number.

Prime factorization: 600 = 2 x 2 x 2 x 3 x 5 x 5, which can be written 600 = (2^3) x 3 x (5^2)

The exponents in the prime factorization are 3, 1 and 2. Adding one to each and multiplying we get (3 + 1)(1 + 1)(2 + 1) = 4 x 2 x 3 = 24. Therefore 600 has exactly 24 factors.

Factors of 600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600

Factor pairs: 600 = 1 x 600, 2 x 300, 3 x 200, 4 x 150, 5 x 120, 6 x 100, 8 x 75, 10 x 60, 12 x 50, 15 x 40, 20 x 30 or 24 x 25

Taking the factor pair with the largest square number factor, we get √600 = (√100)(√6) = 10√6 ≈ 24.494897. (Note: 2 + 4 = 6 and 49 + 48 = 97 so this square root and √6 can be easy to remember.)

User Pjesi
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