Britney scored an 85 on her last math test write the prime factorization on 85
1 answer:
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.
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The easiest way to solve this, is expressing the division as a fraction, and then use divisibility rules to simplify our fraction.
Remember that saying 6476 divided by 12 is the same as . Just like that we have our fraction. Now to simplify it, we are going to use divisibility rules
Remember that to simplify a fraction using divisibility rules, both numerator and numerator must by divisible by the same number.
- Divisibility by 2
A number is divisible by 2 if and only if it ends in 0, 2, 4, 6, or 8. In other words, a number is divisible by 2 if its last digit is even or zero.
Notice that 6476 ends in 6, so it's divisible by 2, and 12 ends in 2, so it's also divisible by 2. Since both the numerator and denominator of our fraction are divisible by 2, we can simplify our fraction dividing both numerator and denominator by 2. To divide by 2, we just need to find the half of each number. The half of 6476 is 3238 and the half of 12 is 6, so we can simplify our fraction as follows:
3238 ends in 8, so it's divisible by 2; 6 ends in 6, so it's divisible by 2. The half of 3238 is 1619 and the half of 6 is 3, so we can simplify our fraction even more:
Now, 1619 does end in zero or an even number, so it's not divisible by 2; similarly, 3 is not even even, so it's not divisible by 2. Let's check if they are divisible by 3
- Divisibility by 3
A number is divisible by 3 if an only if the sum of its digits is 3 or multiple or 3.
Let's check if the numerator of our fraction, 1619, is divisible by 3:
Since 17 is not a multiple of 3, 1619 is not divisible by 3.
Now, let's check if our numerator, 3, is divisible by 3:
3 is a multiple of 3, so its divisible by 3.
Since our numerator is divisible by 3 but our denominator is not, we can't further simplify our fraction.
We can conclude that the result of 6476 divided by 12 is , or expressed as decimal:
.