# ACE_Project_1

```ACE Project 1
p. 14 (4, 7, 13, 15, 28, 30)
4) What factor is paired with 3 to give
24?
•8
▫ 3 * 8 = 24 so 3,8 are factor pairs of 24.
7) Which of these numbers has the
most factors ?
• D - 36
▫
▫
▫
▫
A – 6: 1, 2, 3, 6
B – 17: 1, 17
C – 25: 1, 5, 25
D – 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
13) Which of these numbers are
divisors of 64?
• 2, 8, 16
▫ Divisors are the same as factors because factors
will divide a number evenly, as do divisors.
▫ 64 &divide; 2 = 32 so 2 is a divisor
▫ 64 &divide; 6 = 10.666 so 6 is NOT a divisor
▫ 64 &divide; 8 = 64 so 8 is a divisor
▫ 64 &divide; 12 = 5.333 so 12 is NOT a divisor
▫ 64 &divide; 16 = 4 so 16 is a divisor
15a) A prime number has exactly two factors, 1 and itself.
If you circle a prime number in the Factor Game, your
opponent will receive at most one point. Explain why.
Give some examples.
• In the Factor Game, you are circling proper
factors of a number. The only proper factor of
any prime number is 1. For example, the proper
factor of 17 is 1.
15b) A composite number has more than two factors. If
you circle a composite number in the Factor Game, your
opponent might receive more points than you. Explain
why. Give some examples.
• When choosing a composite number in the
Factor Game you run the risk of the proper
factors of that number adding up to more than
the number itself. Especially for numbers with
numerous proper factors. For example, the
proper factors of 30 are 1, 2, 3, 5, 6, 10, and 15. If
you chose 30 you would receive 30 points and
28) Twenty-five classes from Martin Luther King
Elementary School will play the Factor Game at their
math carnival. Each class has 32 students. How many
game boards are needed if each pair of students is to play
the game once?
• 25 classes * 32 students per class
= 800 students
• You play the game in pairs of 2.
• 800 &divide; 2 = 400 pairs of students
• They will need 400 game boards
for the math carnival.
• 32 students &divide; 2 = 16 pairs per
class
• 16 pairs * 25 classes = 400 pairs of
students
• They will need 400 game boards
for the math carnival.
30) This week Carlos read a book for language arts class.
He finished the book on Friday. On Monday he read 27
pages; on Tuesday he read 31 pages; and on Wednesday he
number of pages each day. The book was 144 pages. How
many pages did he read on Thursday?
• 27 + 31 + 28 = 86 pages Monday,
Tuesday, Wednesday
• 144 – 86 = 58 pages read
Thursday and Friday
• Since he read the same number of
pages Thursday and Friday
• 58 &divide; 2 = 29
• B – 29
• 144 – 27 = 117 pages left after
Monday
• 117 – 31 = 86 pages left after
Tuesday
• 86 – 28 = 58 pages left after
Wednesday.
• Since he read the same number of
pages Thursday and Friday
• 58 &divide; 2 = 29
• B – 29
```