3. What is the highest power of 13 that will divide 9000! without leaving a remainder? (a) 749 (b) 714 (c) 498 (d) None of these

Q: 7. In your own words, describe a procedure for turning an improper fraction, such as , into a mixed…

A: Since there are multiple questions the first question is answered kindly repost mentioning the…

Q: The prime factors (without repetitions) of 17325 are О 2,5, 7 О 3, 7, 11 О 5,5, 7 О 3, 7, 11 О 3,5,…

A:

Q: Show that every rational number has exactly two finite simple continued fraction expansions.

A: To Show : Show that every rational number has exactly two finite simple continued fraction…

Q: How many terms are there in the expansion of (a+b)48 after like terms are collected?

A: This question is related to binomial expansion. We will solve it using given information.

Q: 86- The remainder upon the division of x 98 + 4 by x – 4 in Z, is:

A:

Q: Compute the sum of the first 60 positive integers that are exactly divisible by 4.

A: The numbers divisible by 4 is:

Q: The number of factors of prime numbers are Depends on the prime number None of the mentioned (3 2

A: Given query to find number of factors of a prime number.

Q: 7. Compute the simple contimued fraction expansions for the real numbers. -37/26

A: Given: (1)  3726 (2)   15

Q: What is the smallest positive integer n such that 80325 divides n!

A:

Q: The number of factors of prime numberss are (None of the mentioned Depends on the prime number (2 (3

A: Prime number is only divisible by 1 and that number itself

Q: 4 Compute the quantity, W, using w= -3 W W -5 W = (Type integers or simplified fractions.)

A: Given query is to find indicated vector operation.

Q: What is the sum of the two largest prime factors of 770?

A: You need to express in terms of prime factors.

Q: 1. What are the possible remainders of prime numbers greater than 2 when it is divided by 7? а. 1,…

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Q: a number whose decimal reoresentation repeats is a rational number. true or false

A: A number is rational if and only if its decimal representation is repeating or terminating (i.e.…

Q: 2) How many integers between 1 and 200, including both 1 and 200 are divisible by 4 or 5? 3) How…

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Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: 3. When 4 is wrilten as an improper fraction in sim- plest form, what is the numerator of the…

A: To convert a mixed fraction into an improper fraction, multiply the denominator with whole and add…

Q: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7? Moreover,…

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Q: 5.Find the product of the first five terms of a GP, if its third term is 4.

A:

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: 6.) Find the sum of the first 50 positive integers ending in 6.

A:

Q: Show that n-lis divisible by 8, if n is an odd positive integer

A:

Q: 11. What do you obtain when you raise 27 to the 8/3 power ? * 1/3 of (27 to the 8th power)

A: Any number a can be written as , where b is any natural number. Also, 27 is a cube of 3, so 27 can…

Q: 1. What is the remainder when 65544 - 13 is divided by 8?

A:

Q: How many munbers from 1 till 10000 are NOT divisible by 3, 8, 16 and 7?

A: Here, we have to find the total numbers from 1 to 10000 are not divisible by 3, 8, 16, and 7.  Let A…

Q: Compute the sum of the first 50 positive integers that are exactly divisible by 5.

A: To determine sum of the first 50 positive integers that are exactly divisible by 5.

Q: of all rabbits in a country are in one state and - of the rabbits are in a different state, what…

A: We have that 5/32 of all rabbits in a country are in one state and 2/7 of the rabbits are in a…

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: Find the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5.

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Q: In the Sieve of Eratosthenes for numbers less than 100, explain why, after crossing out al the…

A: Given In the sieve of Eratosthenes for the numbers less than 100 , Explain why, After crossing out…

Q: 1 If 13/7 of all rabbits in a country are in one state and of the rabbits are in a different state,…

A: 237 of all rabbits in a country are in one state and 16 of the rabbits are in a different state.

Q: Find the smallest positive interger x such that 1001 x leaves a remainder of 70 when divided by 315

A: The given statement can be expressed as an expression, which ix given below  315y+70=1001x Now,…

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: Choose the prime factorization of 12 O 2.3 10 O 23.3.5 o 10 12 O2.5.12

A: to find prime factorization  Start by dividing the number by the first prime number 2 and continue…

Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…

Q: The prime factorization of 7007 is 7.11.13 72.11.13 73.11.13 7.11³.13 o

A:

Q: 4. Is 9,521 less than, greater than, or equal to 9,.251? 5. How w many eighths are in 1-? 6. 2+3 x2…

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Q: Prove: If the sum or the difference of two irreducible fractions is an integer, the denominators of…

A: Proof: Let two irreducible fractions are ab and cd Since the fractions are irreducible, (a,b)=1 and…

Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Question 9: Express 52224 and 202125 in term of prime factors

A:

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: 3. There are seven students who always compare their CS test grades. They discovered that either the…

A: It is given that there are seven students who always compare their CS test grades. They discovered…

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

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Q: composite. 10. Suppose that n = 2³ x 5² × 7 × 17³. Give the prime factoriz= (Hint: Do not work too…

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Q: 8. Show that no prime number of the form 4k +3 can divide a number of the form n2 + 1.

A:

Q: 5 Let flx) -5X+3Xh emd gx) = 3X+2X+) in 7[x].Determine the quotient ane remainder upon dividing #00…

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Q: The notions of the greatest common divisor and the least common multiple extend naturally to more…

A: Given: a=21·32·72b=23·33·71c=31·52·73

Q: (17)10 = (?)5 • Using repeated division:

A: A polynomial is an expression that contains variables and coefficients. There are three types of…

Q: 27-8^n a prime? Why?

A: answer is in next step

Q: Show that 19 divides 10*8n-1 + 33n-1 for every positive integer n.

A: Concept: Mathematical induction: For each and every natural number n, mathematical induction is a…