a. Using the divisibility criterion by 11, verify that 11 is an element of the factorization of 322751 in prime numbers. b. Still using divisibility criterions, verify that 322751 is divisible by 77.

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A: Given number is : 613 To find what is the minimum amount of number must divide into 613 to check…

Q: Determine the total number of positive divisors of 2, 000, 000, 000.

A:

Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

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: nd the prime factorization of 238. The prime factorization is

A: Prime factorisation of the number

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

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: Show that 7 divides (1111)³³³³ + (3333)¹¹¹¹

A:

Q: How many divisors of 2310 have excactly three prime factors?

A:

Q: Number of integers n with 4 prime factorizations and divisible by 5, where n less than or equal 2021…

A: we shall consider all the integers less than or equal to 2021, and divisible by 5. And also having 4…

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: Is 193241 divisible by 9? Show if it is or not using a divisibility test. Explain why the…

A: DIVISIBILITY RULE FOR 9:                                         When the sum of digits of a number…

Q: 14) Find a remainder after dividing 2300 on 3.

A: We have, 22≡1 (mod 3) ⇒22150=1150( mod 3) ⇒2300=1(mod 3)

Q: Use this information to compute the prime factorization for the value of each expression given…

A: We need to calculate the prime factorization of (245.352)=2×2×2×2×2×5×7×7×11 i.e.…

Q: that 10348+4303 is divisible by 47. the remainder of 123 is divided

A:

Q: USE A FACTOR TREE OR DIVISION LADDER TO EXPRESS THE NUMBER AS A PRODUCT OF PRIME FACTORS 2475=

A: We have been given a number 2475 and we are required to write it as product of prime factors by…

Q: Find the prime factorization of 285. The prime factorization is

A:

Q: develop a divisibility test for 48

A: Given that a number 48   To check number is divisible by 2,   The last digit 48 id divisible by 2,…

Q: Consider 36, 756, and 1001.

A:

Q: Determine the greatest common divisor of 357 and 221.

A: gcd(357,221)The gcd (greatest common divisor) of a, b is the largest positive number that divides…

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: Which statement explains the accuracy of the students' work? Lina's solution is correct because it…

A: Solution:-

Q: 11+2 + 122n+1 is divisible by 133

A:

Q: 10 9. (15) 35 Analyze Find three equivalent fractions for by multiplying by 3 51 What property of…

A:

Q: 1. Factor 51,948 into a product of primes.

A:

Q: A test for checking computations is called casting out nines. Consider the sum 672+301 5001473. The…

A: Consider the test of casting out nines and the given sum.The objective of the problem is to find the…

Q: 14) You will likely want to have a calculator handy for this question. a) Create several three-digit…

A: a Let, number be 321so, 321-123=198                        =2×99Let another number be 794so…

Q: Find all divisors of 29,601.

A: In this problem we have to find the all divisors of

Q: 1. Find the prime Factorization of 792 using a factor tree.

A:

Q: (a) Determine if the following numbers are prime: 101! + 78, 88! + 55 (b) Is 299 + 1 divisible by…

A: A prime number cannot be divided by any other number except 1 and itself. Now use this definition to…

Q: 1. Find all natural number factors (divisors) of the number 42:

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Q: Label the following number as prime or composite. 37 prime composite If a number is composite, then…

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Q: The prime factorizations of 641, 999

A: We have to prime factorization of 641, 999.

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: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

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: 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) Prime factorize the numbers 10962 and 6188 and then Find the largest common divisor (10962,…

A: