The positive integers that are divisors of 68 are

Q: List all divisors of the following integers. 30

A:

Q: List all divisors of the following integers 42

A: A divisor of an integer a is an integer b, for which a/b is again an integer (which is necessarily…

Q: 2. What are the greatest common divisors of these pairs of integers? (a) 37 x 5 x 7,21 x 3 x 5°

A:

Q: Let n be a positive integer. Show that in any set of n consecutive integers there is exactly one…

A: Let us take any set of n consecutive integers starting from kn+t:…

Q: List all common divisors of each of the following pairs of integers. -40, 24

A: To list common divisors of (-40,24)

Q: List all divisors of the following integers   24

A: All divisiors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

Q: The integers 77 and 105 are relatively prime.

A: Relatively Prime integers: Two integers mand n are called relatively prime if gcd(m,n)=1. Given two…

Q: Suppose 48 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

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Q: The number of positive integers not exceeding 1000 that are not divisible by 8 and not divisible by…

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Q: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

Q: List all common divisors of each of the following pairs of integers 24, 32

A: Given(24,32)To list common divisors of above

Q: List all divisors of the following integers 40

A: List all divisors of the following integers 40

Q: Suppose 50 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

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Q: Prove by Mathematical Induction that 10" - 1 is divisible by 9 for all positive integers n.

A: In proving some statements for all positive integers, we follow the mathematical induction. The…

Q: How many elements are there in the greatest conjugacy class of 5 ?S

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Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: divisors

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Q: List all common divisors of each of the following pairs of integers 42, 45

A: The greatest common divisor of two or more integers, which are not all zero, is the largest positive…

Q: ) Check all the numbers that are divisors. a.) 288

A: see 2nd step

Q: 7. Show that for every natural number n2 1, the integer ) + () +*(;) + - +) +22 +... +2" is…

A: Using binomial theorem:  n0+2n1+22n2....2nnn=n01n·20+n11n-1·21+n21n-2·22....nn1n-n·2n…

Q: List all divisors of the following integers 45

A: The objective is to find the divisors of 45.

Q: Suppose 59 cars start at a car race. In how many ways can the top 3 cars finish the race? ... The…

A: There is total 59 cars.

Q: Show that one of the prime divisors of any three-digit composite number is less than 31 prime, or…

A: A composite integer a has a prime factor p only if p≤a that is if p≥a than there exist another prime…

Q: Prove or disprove: If an integer is divisible by 6 and by 10, then it is divisible by 60.

A: Answer

Q: List all divisors of the following integers 32

A: The objective is to find the divisors of 32.

Q: Find integers μ and λ such that λ48 + μ57 = 3.

A: Find integers μ and λ such that λ48 + μ57 = 3.

Q: 12 belongs to the set of natural numbers

A: The natural numbers (i.e. counting numbers) are numbers which are used for counting and ordering.…

Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers

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Q: Show what the divisors of 120 are and what they add up to.

A: Divisors of 120=1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Q: Suppose that one selects some subset of integers from the set {1, 2, ., 47). What is the smallest…

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Q: Give a recursive definition for the set of all the positive integers that are less than 100 and not…

A: Given: Set of all positive integers that are less than 100. To find: Recursive definition for the…

Q: Find all positive integers n such that the sum of all positive divisors of n is odd.

A: Given the data

Q: How many zero divisors are in Z,, where n = 32547?

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Q: List all divisors of the following integers   210

A: List all divisors of the following integers 210. Divisors of any integer is the set of all numbers…

Q: Show that 5 – V7 is an algebraic number.

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Q: How many negative divisors has the integer 90?

A: The divisors of 90 are all the numbers that we can evenly divide into 90.

Q: find the sum of all integers between 300 and 800 that are exactly divisible by 14

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Q: List all common divisors of each of the following pairs of integers 30, 28

A: Given pairs of integers 30, 28

Q: List all divisors of the following integers   28

A:

Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Show by induction that 21" – 8" is divisible by 13 for all n> 0

A: For the solution follow the next steps.

Q: Show by induction that 19" – 8" is divisible by 11 for all n >0

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Q: Find the sum of the divisors of 120. Generalise the result for an arbitrary natural number M

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Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…

Q: List all common divisors of each of the following pairs of integers   30, -50

A: Given pairs of integers: 30, -50