Since the next prime after 7 is​ 11, the smallest composite number whose prime factors are all greater than​ 7, is ▼     Since this is ▼   less greater than​ 100, there are no ▼   prime composite ​numbers, from 2 to​ 100, whose prime factors are all greater than 7.​ Therefore, ▼   every at least one composite number from 2 to 100 must be a multiple of some prime number less than or equal to 7.

Q: How many integers between 100 and 400 contain the digot 2?

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Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: NOT ALL THE NUMBERS ARE ON HERE!!

A: Solution-: Given data: 18,80,83,295,332,489,503,513,530,544,570,606,793,840,912,980 We want to find…

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: + 220 + 330 + 440 + 550 + 660 (

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Q: If both p and p^2 +8 are prime numbers then show that p^3+4 is also prime number

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Q: Prove by cases For any integer n, n^2 + 5 is not divisible

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Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

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: If O is a natural number then O^2 + 2O + 1 is odd.

A: If O is a natural number then we need to check whether  O^2 + 2O + 1 is odd. The result is given…

Q: How many 5-digit numbers (including leading 0s)are there with no digit appearing exactly two times?

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Q: How many 5- digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9, if repetitions of…

A: Givendigits = 0,1,2,3,4,5,6,7,8,9No.of digits =10

Q: Find all whole#s that leave remainder 3 upon division by 5?

A: The solution is given below:

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: Show that there are no prime triples other than 3, 5, 7.

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Q: True/False: Every integer greater than 1 is divisible by a prime number. True False

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