5. If 552 is divisible by 23, what is the next multiple of 23?
Answers
Answer:
the next multiple of 23 is 575
Answer:
Step-by-step explanation:
Since 23 is a prime number, we are done with the division process. Taking the square root of everything on the outside of the cake we get √552 = (√4)(√6)(√23) = (√4)(√138) = 2√138.
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552 is a composite number.
Prime factorization: 552 = 2 x 2 x 2 x 3 x 23, which can be written 552 = (2^3) x 3 x 23
The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16. Therefore 552 has exactly 16 factors.
Factors of 552: 1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 138, 184, 276, 552
Factor pairs: 552 = 1 x 552, 2 x 276, 3 x 184, 4 x 138, 6 x 92, 8 x 69, 12 x 46, or 23 x 24
Taking the factor pair with the largest square number factor, we get √552 = (√4)(√138) = 2√138 ≈ 23.49468