What is the greatest common factor of 30 and 36

Mathematics

2 answers:

katovenus [111]3 years ago

8 0

Answer:

Step-by-step explanation:

VashaNatasha [74]3 years ago

8 0

<h2>Answer:</h2>

Greatest common factor (GCF) of 30 and 36 is 6.

<h2>Step-by-step explanation:</h2>

<u>We will now calculate the prime factors of 30 and 36, than find the greatest common factor of the numbers by matching the biggest common factor of 30 and 36. </u>

Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

Prime Factorization of 36

Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is:

<u />

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15

Factors of 36

List of positive integer factors of 36 that divides 30 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18

Greatest Common Factor

We found the factors and prime factorization of 30 and 36. The biggest common factor number is the GCF number.

<em>So the greatest common factor 30 and 36 is 6.</em>

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6. Find d.<br><br><br> Please help

Anvisha [2.4K]

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

$tan(35)=\frac{12}{x}$ Isolating x:

$x=\frac{12}{tan(35)}$ so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

$tan(25)=\frac{12}{d+17.1377}$ and simplifying a bit: