Of the following numbers, which has the most factors of 3?
a) 81
b) 270
c) 999
d) 3333

81 has the most factors of 3

Step-by-step explanation:

To conclude which of the following options has the most factors of 3, take each of the number's prime factorization, which will help us solve the problem.

( 1 ) 81 is a composite number and is 9 squared. Knowing that 3 squared = 9, we can say that the prime factorization of 81 = 3 3 3 3, which can also be denoted as 3⁴.

( 2 ) 270 is a composite number. The exponents in the prime factorization are 1, 3, and 1, and therefore it's prime factorization is - 3 5 3 2 3, composed of 3 3s.

( 3 ) If we put all of it together we have the factors 3 x 3 x 3 x 37 = 999. It can also be written in exponential form, with 3 to the power of 3 - hence having 3 factors of 3.

And finally the value 3333 has the prime factorization of 3 11 101, and as you can see it has 1 factor of 3. 81, having 4 factors of 3, is present with the most factors, and therefore is our solution.

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1