1. Find the prime factorization of 111111.

Q: Determine whether there are infinitely many primes that have a remainder of 12 when divided by 25.…

A: Given question is Determine whether there are infinitely many primes that have a remainder of 12…

Q: ) Compute the smallest prime factor of 2197.

A: We have to Compute the smallest prime factor of 2197.

Q: If n is a positive integer, explain why each prime in the factorization 'n² must occur an even…

A: (a) Let p be a prime number that occurs in the prime factorization of n2.   This implies that p…

Q: IS 2371 Prime yes or no? explain?

A: We have been given a number: 2371. To Do:We have to tell whether 2371 is prime or not.

Q: What is the greatest prime you must consider to test whether 5317 is prime? The greatest prime to…

A:

Q: Computer (73112). (Hint: you do not need to multiply out 7³11².)

A: We have to compute .We know thati) is the number of positive divisors of n .

Q: Determine the prime factorization of 4984

A: Find the prime factorization of 4984 as follows.

Q: # 14 please ASAP

A: We need to evaluate 77 (mod 4).By the Fermat’s Little Theorem,

Q: Suppose is an integer satisfying the linear congruence Enter the least residue of a modulo 11210.…

A:

Q: Sum of twin primes is divisible by 2. Select one: O True O False

A:

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

A:

Q: If you randomly pick integers from 1 to 200, how many would you have to pick to ensure that at least…

A:

Q: Match each of the following integers with its equivalent representation in a different base. (123) g…

A: Number system are of the type  Binary decimal with two bits 0 or 1. The decimal number is from 0 to…

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n): decimal =…

Q: Consider 36, 756, and 1001.

A:

Q: What is the decimal integer 1424 in binary notation? Select one: a. 10110001110, b. 10110001111, C.…

A: We are given decimal integer 1424. we have to convert it into binary.

Q: Find all prime numbers between 250 to 350 using Sieve of Eratosthenes.

A: Given The given numbers are .

Q: 2. What are the prime factors for the below numbers and arrange them in a canonical form. a. 17 b.…

A:

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: The binary expansion 0.abcd... means 23 24 and each binary digit a, b, c, d, ... is either 0 or 1.…

A:

Q: 4. Give the prime factorization of the number 468. Use exponents in the final answer.

A:

Q: Find the prime factorization of 345. The prime factorization is

A: Given number is  345   Prime factorization: It is a method to express a number as product of its…

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: 2. Factor 10+1 into a product of primes for k = 1,2,3,4,5.

A: