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Diano4ka-milaya [45]
2 years ago
10

Use the Euclidean Algorithm to demonstrate that 621 and 82 are relatively prime to each other. Explain.

Mathematics
1 answer:
8090 [49]2 years ago
5 0

Answer:

621 and 82 are relatively prime.

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one).

The greatest common divisor of two integers <em>a</em> and <em>b</em> is the largest integer that divides them both.

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:

<em>Given integers a, b find </em>d=gcd(a,b)<em />

The Euclidean algorithm provides a fast way to determine <em>d</em> without knowing the prime factors of <em>a</em> or <em>b</em>. Here is an outline of the steps:

  1. Let a=x, b=y
  2. Given <em>x</em>, <em>y</em>, use the division algorithm to write x=yq+r, \quad 0\leq r\leq |y|.
  3. If r = 0, stop and output <em>y</em>; this is the gcd of a, b.
  4. If r \neq 0, replace (<em>x, y</em>) by (<em>y, r</em>). Go to step 2.

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 until we get a result that lies between 0 (inclusive) and D (exclusive) and is the smallest non-negative number obtained by repeated subtraction.

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.

Applying the above steps,

621-82=539\\539-82=457\\457-82=375\\375-82=293\\293-82=211\\211-82=129\\129-82=47\\\\621=82\cdot7+47

621 = 82\cdot 7 + 47\\ 82 = 47\cdot 1 + 35\\ 47 = 35\cdot1 + 12\\ 35 = 12\cdot2 + 11\\ 12 = 11\cdot1 + 1\\ 11 = 1\cdot11 + 0

The gcd(621, 82) is 1. Therefore, 621 and 82 are relatively prime.

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The volume of the right triangular prism is 153.30 cubic units if the base length of the prism is 8 units.

<h3>What is a triangular prism?</h3>

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

It is given that:

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As we know, the volume of the right triangular prism is given by:

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Here b and l are the base dimensions h is the height of the prism

From the trigonometric ratios:

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1 year ago
HEB has dish soap that costs $2.80 for a 12oz bottle. Fiesta has the same dish soap that costs $2.00 for a 8 oz tube.
s2008m [1.1K]

Answer:

The unit rate at HEB is $0.23 per ounce. The unit rate at Fiesta is $0.25 per ounce. So HEB has the better buy for dish soap.

Step-by-step explanation:

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So for HEB, you should do $2.80/12 oz. This will equal to $0.23 per ounce. For Fiesta, you should do $2.00/8 oz. This will equal to $0.25 per ounce.

To determine which one is the better buy, the lower priced one is better, meaning HEB is the better buy.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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