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ACE Project 1 p. 14 (4, 7, 13, 15, 28, 30)

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**4) What factor is paired with 3 to give 24?**

8 3 * 8 = 24 so 3,8 are factor pairs of 24.

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**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

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**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 ÷ 2 = 32 so 2 is a divisor 64 ÷ 6 = so 6 is NOT a divisor 64 ÷ 8 = 64 so 8 is a divisor 64 ÷ 12 = so 12 is NOT a divisor 64 ÷ 16 = 4 so 16 is a divisor

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**15a) A prime number has exactly two factors, 1 and itself**

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.

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**15b) A composite number has more than two factors**

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 your opponent would receive 42 points.

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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 ÷ 2 = 400 pairs of students They will need 400 game boards for the math carnival. 32 students ÷ 2 = 16 pairs per class 16 pairs * 25 classes = 400 pairs of students They will need 400 game boards for the math carnival.

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**30) This week Carlos read a book for language arts class**

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 read 28 pages. On Thursday and Friday he read the same number of pages each day. The book was 144 pages. How many pages did he read on Thursday? = 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 ÷ 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 ÷ 2 = 29 B – 29

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