1) 1. Determine which of the following integers are prime, if they are composite show the prime factorization. a) 7902 b) 202 c) 83 d) 241 e) 331 f) 439

Q: Find the number of positive integer divisors of a) 36 b) 99 c) 144 d) 2-3-5-7-11-13-17-19 e)…

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Q: 1): For which values of n is n div 5 = -6? A): n = -30, -29, -28, -27, and -26. B): n = -30, -15,…

A: see below the answer and explanation

Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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Q: 9. using prime factorisation, find the HCF of (i) 2622, 1653 (ii) 1891, 1098 10.Check whether 12"…

A: We have to find out hcf

Q: DOference of twin primes is not divisible by 2. :Select one True False

A: There are infinitely many twin primes, or pairs of primes that differ by 2. For example, 3 and 5, 5…

Q: 1. Let A = {m,2m,3m,...} where meP; that is, Aconsists of the positive integers of т. Find: a) ANA,…

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Q: 8) The number 4050 can be factored into prime divisors as: 2 x 3 x 3 x 3 x 3 x 5 x 5 a) Determine…

A: We have to solve

Q: Want a rigorous proof   Prove that The set of prime numbers has no largest element.

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Q: 10. How many positive integers between 100 and 999 inclusive a) are divisible by 7? b) are not…

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Q: Which of the following represents the expression as a single power (104) (107) 10⁹

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Q: Prove by contraposition the following theorem For integers: if n = 2 m, then n² = 4 m² (i.e., if a…

A: Introduction: Numbers divisible by 4 are those that have zeros or multiples of 4 as the last two…

Q: highest prime that might need to be checked to find the prime factorization of the number. Then,…

A: We need to determine highest prime that might need to be checked to find prime factorisation.

Q: modulo 5   B).  Evaluate 31mod5

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Q: 8.  Identify the prime factorization of the... GCD of 20,270,250 and 13,728. LCM of 20,270,250 and…

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Q: If p - 2, p , and p + 2 are all prime, the only possible value of p is A) 3 B) 5 C) 59 D) 89

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Q: Find a) the greatest common divisor (GCD) and b) the least common multiple (LCM). 100 and 120 a) The…

A: Solution

Q: EXTENSIONS Given any seven different non-zero digits, what placement of the digits in a two-digit…

A: Let's consider the seven non-digit numbers to be: 3, 4, 5, 6, 7, 8, 9. A four-digit number and…

Q: 1. What are the quotient and remainder, respectively, when -97 is divided by 13? a) -7 and -6 b) 8…

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Q: *) The following number has a missing digit x, n = 13645x04142250 a) If n is divisible by 9, then x…

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Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

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Q: 1) A: Provide one example of each of the following: A prime number less than 30: A number that is…

A: (a) The aim is to find examples of the given statements.(b) To find the prime factorization of and…

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: . Select the sets) of numbers that are subsets of rational numbers. a. Integers only b. Whole…

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Q: How many positive integers less than 28716 are a) divisible by 4? b) divisible by 5? c) divisible…

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Q: 5. Find the number of positive integers less than 700 that are divisible by 3 but not divisible by…

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Q: dentify each number as prime or composite. Then list all the factors. 5) 2 6) 37 7) 27 8) 54 9)…

A: Prime number : the natural number which has factors 1 and number itself is called prime number.…

Q: 3. Determine if the the number 132 is perfect, deficient or abundant. Show all work.

A: A number is said to be perfect if sum of its proper divisors is equal to the nunber.  Deficient if…

Q: A). For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343…

A: Let xyz is there digit number x has choice 1,2,...,9 while y and z has choice 1,2,...9  So that…

Q: 1. Find the number of integers between 1 and 10,000 inclusive that are a) Divisible by at least one…

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Q: 1. Find the sum of the positive integer divisors of a) 35 e) 2-3-5-7-11 b) 196 f) 25345³7²11 c) 1000…

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Q: What are the prime factors of 48

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Q: a) Describe a procedure for finding the prime factorization of an integer.b) Use this procedure to…

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Q: 42. If m is a positive prime number, how many positive integer divisors does m0 have? (A) One (B)…

A: To solve the given problem, we use the result of  prime number in number theory.

Q: Each of following has 9 as a factor except: A) 18,018 B) 18,081 C) 81,180 D) 81,181

A: A) 18,018 B) 18,081 C) 81,180 D) 81,181To find which of the following does not have 9 as a factor

Q: a. Using the divisibility criterion by 11, verify that 11 is an element of the factorization of…

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