數學疑問(please help me)

16.Show that 361 is not a prime number.
Definition of prime number: the factor of the number can only be 1 and itself
361 = 19*19
for 19=/=361 and 19=/=1
Hence, 361 is not a prime number


23.Find the unit digit of the expression (5x2)+(5x4)+(5x6)+(5x8)+...+(5x998).Briefly explain your answer.{(Hint)Conider the valur of the expression in each pair of brackets.}
(5x2)+(5x4)+(5x6)+(5x8)+...+(5x998)
= 5*(2+4+6+...+998)
= 5*[(2+998) + (4+996) + ... + (498 + 502) + 500]
= 5*(1000)(1000)/2
= 250000



24.Find the unit digit of the expression 1x2x3x...x2009x2010.Briefly explain your answer.{(Hint)Consid the product of the first 5 integers.}

The unit digit is 0 because when any number times 2010, the last digit must be 0.


Concept Builder

Determine whether each of the following statements is correct or not.
1.The factors of 24 are 1,2,4,6,12and24. Yes/no
No. since 24 also = 3*8

2.The H.C.M. of 64 and96 is 32. Yes/no
Yes, since 64 = 2*32 and 96 = 3*32 for 2=/=3

3.We can find the highest common multiple of 2 positive integers. Yes/no
No, since there are infinite integer

4.We can find the least common factor of 2 positive integers. Yes/no
Yes, since the least common factor must be 1.

6. (a) Write down the first 8 multiples of 15.
15,30,45,60,75,90,105,120
(b) Write down the first 8 multiples of 20.
20,40,60,80,100,120,140,160
(c) Using the resuls in (a) and (b),write down the common multiples of 15 and 20.
60,120
(d) Hence find the L.C.M. of 15 and 20.
L.C.M. = 60

13.48 boys and 60 girls joined a treasure hunt competition.The teacher wants to group the students into as many groups as possible,so that each group has the same number of boys and the same number of girls. What is the maximum number of groups?What are the numbers of boys and girls in each geoups?
Let there are x groups
48:60 = 4:5
Hence, at least there should be 9 people in a group, for 4 boys and 5 girls.
Number of groups = 48/4 = 12