LEARNING ACTIVITIESUALA Give the prime factorization of these numbers using the factor tree method.242 1243 1684 1265. 2726 234B. Give the prime factorization of these numbers using the continuous division method.842 1123. 165C Determine whether each number is a prime or a composite mumber1276 1711 7882 637.4712 6123 1108 2313. 8704 2129 5114. 109S. 32410. 23815. 3200Shot on Y11

1. Write the prime factorization of 24 using factor tree method.

Answered: A. Give the prime factorization of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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12 7 9 16 71 50 Look at some decimal expressions of fractions such as 1, 3, 5, 8, 15, 2014 50 by carrying out long divisions or using your calculator (Careful, calculators can give mis- leading results!), and see which numbers have a terminating decimal expression, while paying attention to the prime factorisation of the denominator. Hint: Take a terminating decimal expression and see what happens when you convert it to a fraction in lowest terms. (Don't include this part in your homework submission.) Now come up with a conjecture for which fractions have a terminating decimal expres- sion. Your conjecture should be of the following form: Let a, beN with b>1 and with gcd (a, b) = 1. Then 음 has a terminating decimal expression iff .... Now prove your conjecture. Note that this is an "if and only if" statement, requiring proofs for both implications.
L
1.) Factor 51, 948 into a product of primes.
Identify the smaller root
Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number. Show all your work.
5. Look at some decimal expressions of fractions such as 325' 5' 15' 20' 14' 50 1 7 9 16 71 50 91 by carrying out long divisions or using your calculator (Careful, calculators can give mis- leading results!), and see which numbers have a terminating decimal expression, while paying attention to the prime factorisation of the denominator. Hint: Take a terminating decimal expression and see what happens when you convert it to a fraction in lowest terms. (Don't include this part in your homework submission.) Now come up with a conjecture for which fractions have a terminating decimal expres- sion. Your conjecture should be of the following form: Let a, b EN with b > 1 and with gcd(a, b) = 1. Then a has a terminating decimal expression iff .... Now prove your conjecture. Note that this is an “if and only if” statement, requiring proofs for both implications.
7 A. B. C. D PLEASEEEEE
4. Prove that every integer is either even or odd. Remark: Make sure that you are using the definitions of "even" and "odd" that I gave in class. Hint: Use the Division Theorem to divide an arbitrary integer by 2 with remainder.
Part 5 of 5 Complete the given factor tree and then give the resulting prime factorization of 85,800. At each level in the factor tree at least one factor is given to you. Type the missing factors. 85,800 100 858 2 50 429 2 25 3. 143 5 5 11 13 Write the prime factorization of 85,800. Use exponents to show any repeated prime factors. 85,800 =D (Type your answer using exponential notation.)
5 7 5 2 6' 18' 9' 72 a. Determine the LCD of the above by inspection. LCD by inspection b. Determine the LCD of the above by division of prime numbers. LCD by division of prime numbers Q Search Prev 1 of 10 -

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