Combinatorics | Number Theory Answers

A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)

B. Determine if each of the following numbers is a prime or composite.

6.  828

7. 1666

8. 1781

9. 1125

10. 107

C. Find the greatest common divisor of each of the following pairs of integers.

11. 60 and 100

12. 45 and 33

13. 34 and 58

14. 77 and 128

15. 98 and 273

D. Find the least common multiple of each of the following pairs of integers.

16. 72 and 108

17. 175 and 245

18. 150 and 70

19. 32 and 27

20. 540 and 504

 Define the multiplicative inverse in modular arithmetic and identify the multiplicative inverse of 6 mod 13 while explaining the algorithm used.

Find the remainder when 7^21+49^21+343^21+2401^21 is divided by 7^20+1

In horse racing, a trifeta is a type of bet. To win a trifeta bet, you need to specify the horses that finish in the top three spots in the exact order in which they finish. If eight horses enter the race, how many different ways can they finish in the top three spots?

 Polya described four steps in the solving of a mathematics problem. Here is a problem: A classroom has 2 rows, each with 8 seats. Of 14 students, 5 always sit in the front row, and 4 always sit in the back row, and the rest sit in either row. In how many ways can the students be seated?

6.1.1 Use three different types of representations to model the problem

6.1.2 Now use the steps of Polya to solve this problem. You must explain in detailwhat you are doing in each step

Coach Tab will select 3 girls and 3 boys for

the mix volleyball games. If he has 7 girls

and 8 boys on the pool, how many different

combinations can he have?

How many different rectangles can be made, whose side lengths in centimeters are counting numbers and whose area is 1159 cm2.?

Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?

A={1,2,3,4} and R={(1,2),(3,4),(2,1)}.find transitive closure of R

Consider the simple problem of placing four coloured balls: red, blue, green and white in 15

boxes. What are the numbers of distinct ways in which the balls can be placed in these

boxes, if each box can hold only one ball? Also write the generalized formula of this

numerical result.