10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 = 5'has two divisors (1 and 5 itself) 6 = 2' x 3' has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). If a number n = p," xp x P, x x P1×P,where p,, P P3- P-r Pare prime numbers and a,, a, a,- a a,are the corresponding exponents of the prime numbers, how many divisors doesn have ?
10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 = 5'has two divisors (1 and 5 itself) 6 = 2' x 3' has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). If a number n = p," xp x P, x x P1×P,where p,, P P3- P-r Pare prime numbers and a,, a, a,- a a,are the corresponding exponents of the prime numbers, how many divisors doesn have ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Please help me solve these questions. Thanks
![10. Every positive integer greater than 1 has at least two divisors and can be written as a unique
product of some prime number/s with exponents. For example,
5 = 5'has two divisors (1 and 5 itself)
6 = 2' x 3' has four divisors (1, 2, 3 and 6)
16 = 2* has five divisors (1, 2, 4, 8 and 16).
If a number n = p," × P × P,' x . x pPX Pwhere p,, P P3- P-r' Pare prime
numbers and a,, a, a, a a,are the corresponding exponents of the prime numbers, how
many divisors does n have ?
11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
12. [Bonus] In how many ways can 7 people A, B, C, D, E, F and G be seated at a round table so
that no two of A, B and C sit next to each other?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93cd9a1d-4aef-4349-8452-e90cf27dc453%2F340f8d90-d131-4dfe-9263-4c8833d2ca37%2F1dvvt9g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. Every positive integer greater than 1 has at least two divisors and can be written as a unique
product of some prime number/s with exponents. For example,
5 = 5'has two divisors (1 and 5 itself)
6 = 2' x 3' has four divisors (1, 2, 3 and 6)
16 = 2* has five divisors (1, 2, 4, 8 and 16).
If a number n = p," × P × P,' x . x pPX Pwhere p,, P P3- P-r' Pare prime
numbers and a,, a, a, a a,are the corresponding exponents of the prime numbers, how
many divisors does n have ?
11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
12. [Bonus] In how many ways can 7 people A, B, C, D, E, F and G be seated at a round table so
that no two of A, B and C sit next to each other?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
