a) Find the prime factorization of 4680. Be sure to show your work. b) Find the smallest positive integer divisible by 5 and 7 that is a square, a cube, and a fifth power (Just give the prime factorization). Be sure to explain your steps.

Q: If you want to check that 613 is a prime number using the test for primality, what is the minimum…

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

Q: DOference of twin primes is not divisible by 2. :Select one True False

A: We Know that Two prime numbers are called twin primes if there is present only one composite number…

Q: Build the least common multiple of A and B using the example/method in module 8 on page 59860. Then…

A:

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: What is the prime factorization of 72?

A:

Q: If a, b are two distinct prime number than a highest common factor of a, b is: (2 ab

A: HCF of two numbers is found out by taking common prime factors from both the numbers the…

Q: If N =30 -1. Is N is divisible by 125?

A:

Q: ) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively.…

A:

Q: Find the Prime Factorization of 648, 1056, and 1496. Provide at least one divisibility test for each…

A:

Q: Determine the prime factorization of 4984

A: Find the prime factorization of 4984 as follows.

Q: in pascals triangle which row has a sum of 65536?

A: We know that the sum of every row of Pascal's triangle is twice of the last row's sum.  And it is…

Q: The Great est Common Divisor of two prime numbers a and b is

A: Given : a and b are two prime numbers To find : Greatest Common Divisor of a and b.

Q: How many numbers do I need to test to see if 421 is a prime

A: Given query is to check 421 is a prime number or not.

Q: (a) How many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, and 7, if each digit…

A:

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

A:

Q: 16. Devise a way of checking whether or not a number is divisible by 24. Test your method on 36 and…

A: 16

Q: 7. What might be an easy way to use base 10 blocks to illustrate multiplying a number by 10?

A: Let their are 10 blocks. each block contains 2 balls.   So total number of balls is…

Q: Show that we can easily factor n when we know that n is the product of two primes, p and q, and we…

A:

Q: The smallest prime number is: 1) 3

A: The smallest prime number defined by modern mathematicians is 2 . To be prime, a number must be…

Q: Find the prime factorization of the composite number. 252 O 22 x 32 x 7 24 x 7 34 x 7 23 x 32 x 7

A: Concept: ⇒Divide the number with the smallest prime number which gives remainder 0. ⇒After dividing…

Q: Suppose that n=24.35.112.133. How many divisors does n have?

A: Given,  n = 24 35 112 133 Then (4+1)(5+1)(2+1)(3+1) = 5×6×3×4=360 It has 360 number of divisors

Q: what are ALL the six-digit numbers of the form 47_8_6 that are divisible by 24?

A: The six-digit number has form 47__8__6

Q: Does 7|6265? Using the method we learned in class, show how you can tell without actually dividing…

A:

Q: The smallest prime number is: (3 (2. 1.

A: A prime number is a whole number greater than 1, which is divisible by 1 and itself only.

Q: The prime factorization of 1001 is 73.11.13 72.11.13 7.11.13 7.113.13 O

A: Prime numbers are the numbers that have only 1 and the number itself as factors. For example, 3 and…

Q: The prime number 8191 is a

A: The smallest Mersenne prime p such that the Mersenne number M(p) = 2^p - 1 is composite. TAKE P=13…

Q: Explain your or own word or write the formula for how to find a standard divisor?

A: The formula to find a standard divisor is given below.

Q: The prime factorizations of 641, 999

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

Q: Build the least common multiple of A, B, and C using the example/method in module 8 on page 59&60.…

A:

Q: If x is the greatest prime factor of 39 and y is the greatest prime factor of 72, what is the value…

A:

Q: 2. For which odd primes p is 11 a

A: If p is a prime, then by Fermat's Little Theorem

Q: Without using a calculator, test for 60,330 for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11 Is…

A:

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: Classify the given statement as true or false ( picture)

A: We have to classify the statement is true or false: If a number is divisible by 6, then it is…

Q: Choose the prime factorization of 120. O 22.3.10 O 23.3.5 o 10 12 O 2.5 12

A:

Q: |(3) Find the prime factorization c. 1575

A: Prime factors

Q: Does 7|6265? Using the method, we learned in class, show how you can tell without actually dividing…

A:

Q: 2. Give an example of a whole number that is not a natural number.

A: Set of natural number is {1,2,3,4,...} Set of whole number is {0,1,2,3,....}

Q: Evaluate the Mersenne number M17, and determine whether it is prime.

A: Mersenne number  M(n)=2n-1 Given M(17) To evaluate

Q: How many positive divisors does 4984 have?

A: we have to find the number of positive divisors of the number 4984  so, for that, we will first…

Q: Find the exact value of the expression. 6251/In 5

A:

Q: How many factors are there in 8^5 x 8^9? Answer clearly

A: We use  am.an= am+n

Q: What is the value of the smallest composite number with exactly 3 distinct prime num- ber in its…

A:

Q: (3) Find the prime factorization c. 1575

A: The given number is: 1575

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

A: answer is in next step

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

A:

Q: How many of the calculations are prime factorizations of 1260? i. 14 x 30 x 3 ii. 7 x 60 × 3 iii. 42…

A:

Q: Complete the given factor tree and then give the resulting prime factorization of 85,800.

A: Prime no.are those no. Which have only two factors ,  i.e . 1 and itself Please note : you have…

Q: 1.What is the smallest number that can be exactly divided by 2, 3, 4, 5  and 8 ? 2.What are the…

A: To answer the given questions.

Q: Lucy is trying to determine if 233 is a prime number by dividing 233 by smaller primes. (i) What is…

A: It is given that, Lucy is trying to determine if 233 is a prime number by dividing 233 by smaller…