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Answer:
Step-by-step explanation:
Just so you know, for your information, composite numbers have more than <em>two</em> factors, and prime numbers have EXACTLY two factors [1 and itself (that number)].
* A common mistake is that people make is that they say that all even numbers are composite, and that is false because there are odd numbers that are PERFECT SQUARES and can be divided evenly without leaving a remainder. So, using the Prime Factorization Method, you can do this in two structures:
- Ladder Diagram
- Factor Tree
Factor Tree
85
/ \
17 5
Ladder Diagram
17|<u>85</u>
5|<u>5</u>
1
In the Ladder Diagram, when you are down to 1, you know that factorization is over and there is nothing else to do.
So, with that being said, the prime factorization of 85 is 17 × 5.
I am joyous to assist you anytime.
A generic odd number can be written as
Since there is an odd number every two numbers, three consecutive odd numbers will be
Now let's make up the equations: the sum of the first two is
And 27 less than 3 times the largest is
These two must be the same, so we have
Subtracting 4k and 3 from both sides gives
Which means that the problem has no solution.
To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even
On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).
So, the left hand side is even, and the right hand side is odd. They can't be the same number.