Chapter 4: Q34E (page 273)
How many divisions are required to find gcd(21,34) using the Euclidean algorithm?
7 divisions are required to find gcd(21,34) .
Over 22 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
The value of the Euler -function at the positive integer is defined to be the number of positive integers less than or equal to that are relatively prime to. [Note: is the Greek letter phi.]
Find these values of the Euler -function.
a)role="math" localid="1668504243797" b)role="math" localid="1668504251452" c)role="math" localid="1668504258881"
Using the method followed in Example 17, express the greatest common divisor of each of these pairs of integers as a linear combination of these integers.
a) 10,11 b) 21,44 c) 36,48 d) 34,55 e) 117,213 f)0,223 g) 123,2347 h) 3454,4666 i) 9999,11111
Use exercise 37 to show that the integers and are pair wise relatively prime.
Find the prime factorization of each of these integers.
a.)39 b) 81 c) 101 d) 143 e) 289 f) 899
Find the prime factorization of each of these integers.
a.) 88 b.) 126 c.) 729
d.) 1001 e.) 1111 f.) 909,090
What do you think about this solution?
We value your feedback to improve our textbook solutions.
