Question

1. Tell whether the number 47 is prime

or
composite. Then write all the factors of the number.
2.Tell whether the number 81 is prime
or
composite. Then write all the factors of the number

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Answer 1

1. The number 47 is prime. The only factors are 1 and itself. We can check by dividing 47 over the list of primes smaller than 47. To be more efficient, we can stop once we reach sqrt(47) = 6.85. So we only need to check the primes {2, 3, 5} to show they are not factors of 47 to show that 47 is prime.

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2. The number 81 is composite. It is not prime because it has factors other than 1 and itself.

There are 5 factors and they are

1, 3, 9, 27, 81

Note how each factor listed is a power of 3 (1 = 3^0, 3 = 3^1, 9 = 3^2, 27 = 3^3, 81 = 3^4)

The prime factorization of 81 is

81 = 3*3*3*3 = 3^4

Answer 2

Answer:47 is a prime and 81 is a composite

Step-by-step explanation:47={1,47}

81={1,3,9,18,27,81}