Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496)

(a)

(b)

(c)

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

                                  Given integers , find

Here is an outline of the steps:

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .

(b) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .

(c) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.