Express the following numbers as exponents of prime factors. 576
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Answered by
4
Answer:
576=2*2*2*2*2*2*3*3=2^6*3^2
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8
Answer:
576 is a composite number.
Prime factorization: 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3,
which can be written 576 = (2^6) x (3^2)
The exponents in the prime factorization are 6 and 2. Adding one to each and multiplying we get (6 + 1)(2 + 1) = 7 x 3 = 21. Therefore 576 has exactly 21 factors.
Factors of 576: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
Factor pairs: 576 = 1 x 576, 2 x 288, 3 x 192, 4 x 144, 6 x 96, 8 x 72, 9 x 64, 12 x 48, 16 x 36, 18 x 32 or 24 x 24
576 is a perfect square. √576 = 24
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