The number 42 has the prime factorization 2- 3. 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1· 42, 2- 21, 3· 14, and 6 - 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P2 P3P4, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f. Then f, corresponds to a subset of {P1 P2: P3 Pa, and f, corresponds to the complement of that subset.) (c) If n = P, P2P3PaPs, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n= Pi 2 P where the p, are distinct prime numbers, how many ways can n be written as product of two positive integer factors?

The number 42 has the prime factorization 2- 3. 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1· 42, 2- 21, 3· 14, and 6 - 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P2 P3P4, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f. Then f, corresponds to a subset of {P1 P2: P3 Pa, and f, corresponds to the complement of that subset.) (c) If n = P, P2P3PaPs, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n= Pi 2 P where the p, are distinct prime numbers, how many ways can n be written as product of two positive integer factors?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Explain why in any digraph, the sum of all the in-degrees must equal the sum of the out-degrees.

A: To prove, the sum of all the in-degrees must equal to the sum of all out-degrees. In-degree of a…

Q: when will the product or quotient of 2 integers be positive? when will it becomes negative?

A: Note: We have the integers like -7, 5 ,-4 etc. We have to consider three possible combinations for…

Q: What is the minor of element a23 -2 5 -2 5 3 - -3 4 4,

Q: Select all expressions that are equivalent to each other. O A (3 x 3)" O B. (3x3")? O C. O C. 9(3)2…

Q: What is the coefficient of the term 13a in expression 13a+6b

A: Given expression is 13a+6b Here the variables are a and b And the constants associated with these…

Q: what is the answer of [8+(12-6)] times 5

Q: When multiplying and dividing integers with different signs the answer will be

Q: What number has a remainder of 2 when divided by 3, a remainder of 3 when divided by 5 and a…

Q: Explain why ( – 9 ) ½ is not a real number, but – 9 ½ is a real number.

Q: 17. Write each number in scientific notation. (a) 367, 000, 000 (b) 0.000003 18. Multiply and…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Why must n2 r in the notation nCr?

A: Topic = Algebra

Q: In(8x) + In 4x? – In(16x)

A: Please refer the attached image for complete solution.

Q: state whether the number is rational or irrational 3√-256

A: Given number, Now, we factor 256 such that one of its factors is a perfect cube.

Q: Given the graph of the polynomial function, determine its equation: 6- 4 2- 0 -2- -4- H 2 3 4 X

Q: what is 5000 +900+90+2+0.8

Q: 4. Evaluate 1 L-1 (4s² – 8s)

Q: May I ask why there is a plus 8 in the final answer?

A: We have to explain why there is 8 in final answer.

Q: Find the formula for 1+2-3+4-5...

Q: What is the integer of 60 feet below sea level

A: Result The integer that represents the depth is -60.

Q: When an integer n is divided by 6, the remainder is 5. What are the possible values of the remainder…

A: From the statement, we can say that

Q: s the answer to 25-3(5+2) equal to 112, 12, 8, or 4? Move the parentheses to create three statements…

A: To determine whether the answer to equal to 112, 12, 8, or 4.

Q: There is a number 61 on a whiteboard. Every minute a number is erased and another number is written…

Q: What is the number halfway between 3 - 1/3 and 2 + 5/7 ?

A: Average

Q: Raul and Mandy both received a math assignment. Part A. Raul's assignment is to write a numerical…

A: There are two problems given, in which we need to match the correct Mathematical problem to its word…

Q: (-5+z) is positive, but (-6+z) is negative. What number could z be?

Q: Omar wrote 3 + (4 X 6) to represent the phrase "3 more than the product of 4 and 6." Did Omar need…

A: In mathematical expressions, there is a order in which each of the operators are to be evaluated.…

Q: Compute the value of these expressions: 1x8+1,12x8+2 and 123x8+2

A: Given the expressions:1x8+1,12x8+2 and 123x8+2

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

The number 42 has the prime factorization 2· 3. 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1. 42, 2· 21, 3 · 14, and 6· 7. Answer a-d below without regard to the order of the
factors.
(a) List the distinct ways the number 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.)
(b) If n = p, P, P3PA where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f,. Then f, corresponds to a subset of
{P1 P2. P31 P4}, and f, corresponds to the complement of that subset.)
(c) If n = p, P, P3PAP5, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
(d) If n = p, P, ... Pr where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Which operation should be performed first to simplify the following? 15 -9 + (-3)? Subtract 9 from 15 Divide 9 by (-3) Multiply 2 times (-3) Square (-3)
The question is in the photo
If a and b are both negative integers, which is greater, (a+b)2 or a2 + b2?
what is 28 over 12 in simplest form
what are all of the factors of the number 35?
Can you evaluate 16+2 to the power of 3.
On a blank sheet of paper (lined or not), write any two different positive integers less than 10. In other words, two different single digit positive whole numbers. (Yes, that is redundant because whole numbers are positive.) Use those two numbers to create two factors, (x- a) and (x - b), where a and b are your two numbers. (If you work together with others on this, which is ok for this assignment, be sure each of you chooses different numbers.) Multiply your factors to create a quadratic in standard form. Next write as a function: f(x) = x^2 - bx + c Now create a quadratic equation by changing f(x) to zero: O = x^2 - bx + c
how would you be able to tell if a number is divisible by 15 without dividing?
What are the factors
Select your answer Simplify: O 1 2x-14 I+7 I-4 2x+7 2+1 I-7 I+2 x²+4x-21 x²-49 8 2x-14 (15 out of 20)
Juan and David were trying to describe parts of the expression 5a + 2b + c. Juan said, "The entire expression is the product of 3 factors." David said, "The entire expression is the sum of 3 terms." Who is correct? Choose 1 answer: Only Juan Only David Neither student is correct. Both students are correct.
Collect like terms and arrange in descending order -6 + 9x + 1/2 x3 + 8 - x + 8/3 x3