Explanation Given information: The given numbers are 6664 and 765 . Formula used: Division algorithm: Let a be an integer and d be a positive integer. Then, there are unique integers q and r with 0 ≤ r < d such that a = d q + r , here, q is the quotient and r is the remainder. So, q = a div d and r = a mod d . The greatest common divisor of two numbers a and b is the integer d which satisfies the following properties: d | a and d | b For all integers c , when c | a and c | b , then c ≤ d . Calculation: To find the greatest common divisor, use the Euclidean algorithm. Step 1: 6664 = 765 × 8 + 544 ⇒ 544 = 6664 − 765 × 8 Step 2: 765 = 544 × 1 + 221 ⇒ 221 = 765 − 544 × 1 Step 3: 544 = 221 × 2 + 102 ⇒ 102 = 544 − 221 × 2 Step 4: 221 = 102 × 2 + 17 ⇒ 17 = 221 − 102 × 2 Step 5: 102 = 17 × 6 + 0 So, 17 is the remainder

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ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 8.4, Problem 26ES

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The greatest common divisor of 6664 and 765 and express it in a linear combination of two numbers.

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Chapter 8.4, Problem 25ES

Chapter 8.4, Problem 27ES

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Chapter 8 Solutions

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The greatest common divisor of 6664 and 765 and express it in a linear combination of two numbers.

Solution Summary: The author explains how to calculate the greatest common divisor, using the Euclidean algorithm.

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To calculate: The greatest common divisor of 6664 and 765 and express it in a linear combination of two numbers.

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Chapter 8 Solutions

To calculate:

The greatest common divisor of 6664 and 765 and express it in a linear combination of two numbers.