Answer to Question #200360 in Combinatorics | Number Theory for Adrienne Buatona

Question

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

Answer 1

Solution:

(A) Determine if 1781 is divisible by 3, 6, 7, 8, and 9

1781 has 1 at one's place, so it is not divisible by 2.

1+7+8+1=17 which is not divisible by 3, so 1781 is not divisible by 3.

So, it is not divisible by 3, 6, 8, 9.

Now, divisibility by 7:

178 - 1x2 = 178-2=176

176 is not evenly divisible by 7, so 1781 is not divisible by 7 either.

(B) Prime factorisation of each number:

Thus, 828, 1666, 1781, 1125 are composite numbers, while 107 is prime.

(C) Prime factorisation of each pair:

Thus, GCD of

(60, 100) is 20

(45, 33) is 3

(34, 58) is 2

(77, 128) is 1

(98, 273) is 7

(D) Prime factorisation of each pair:

Thus, LCM of

(72, 108) is 2 x 2 x 2 x 3 x 3 x 3 = 216

(175, 245) is 5 x 5 x 7 x 7 = 1225

(150, 70) is 2 x 3 x 5 x 5 x 7 = 1050

(32, 27) is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 864

(540, 504) is 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 = 7560