Name
Date
Lesson 1 Enrich
Factors and Multiples
Find the greatest common factor for each number pair.
1. 18 and 24
2. 20 and 30
3. 12 and 14
4. 35 and 45
5. 36 and 54
6. 42 and 90
7. 51 and 85
8. 44 and 66
Find the least common multiple for each number pair.
9. 16 and 24
10. 20 and 25
11. 8 and 10
12. 15 and 20
13. 6 and 9
14. 10 and 12
15. 14 and 21
16. 21 and 35
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Grade 4 • Chapter 8 Fractions
Name
Date
Lesson 2 Reteach
Prime and Composite Numbers
Jeanne is organizing her books in a bookcase. There are the same
number of books in each row. If Jeanne has 16 books, how many
ways can she arrange them?
You need to find all the factors of 16 to find out how many ways
Jeanne can arrange her books.
1 × 16 = 16
or 16 × 1 = 16
16
1
8
2 × 8 = 16
or 8 × 2 = 16
2
4
4 × 4 = 16
4
The books can be arranged in five ways, 1 × 16, 16 × 1, 2 × 8, 8 × 2,
or 4 × 4. So, the factors of 16 are 1, 2, 4, 8, and 16.
A number like 16 that has more than two factors is a composite number.
A number that has only two factors is a prime number.
The factors of 2 are 1 and 2.
2 has exactly two factors, 1 and 2, so it is a prime number.
Find the factors of each number. Then tell whether the number is
composite or prime.
1. 4
2. 9
3. 7
4. 27
Solve.
5. Design a bulletin board with rows and columns for
32 drawings. Decide if 32 is a prime or composite number.
List all the ways to arrange the drawings.
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Grade 4 • Chapter 8 Fractions
Name
Date
Lesson 2 Enrich
Prime and Composite Numbers
“Air” + “Toss the Knees” That’s how to pronounce the name of an
ancient Greek thinker — Eratosthenes! He figured out a good way to
sort prime numbers and composite numbers. Follow these directions
to try out his method.
1
2
3
4
5
6
7
8
9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
Directions
1. Cross out 1.
2. Circle the number 2, and then cross out every multiple of 2.
3. Circle the number 3, and then cross out every multiple of 3.
(Be sure to count the numbers that are already crossed out,
like 6.)
4. Notice that 4 is already crossed out.
5. Circle the number 5, and then cross out every multiple of 5.
6. Find the next number that is not crossed out – it’s 7. Circle the
number 7, and then cross out every multiple of 7.
7. Continue the same process until you have circled all the prime
numbers and crossed out all the composite numbers.
8. List the prime numbers less than 50.
If you would like to know more about Eratosthenes, you can read about
him in The Librarian Who Measured the Earth, by Kathryn Laskey.
Grade 4 • Chapter 8 Fractions
57
Name
Date
Lesson 1 Reteach
Factors and Multiples
Find the factor pairs for 18.
Think of multiplication equations that result in a product of 18.
1 × 18 = 18
1 and 18 are a factor pair of 18.
2 × 9 = 18
2 and 9 are a factor pair of 18.
3 × 6 = 18
3 and 6 are a factor pair of 18.
1 and the number itself are
factor pairs for any number.
So, the factor pairs for 18 are 1 and 18, 2 and 9, and 3 and 6.
Determine whether 104 is a multiple of 8.
One way: divide 104 by 8
13
8) 104
–8
24
–24
0
Another way: skip count by 8
104 can be divided
evenly by 8, with no
remainder. So, 104
is a multiple of 8.
8, 16, 24, 32, 40, 48, 56, 64, 72, 80,
88, 96, 104
You can count by 8
to get to 104, so 104
is a multiple of 8.
Find the factor pairs for each number.
1. 9
2. 28
3. 31
and
and
and
and
and
and
For exercises 4–11, write yes or no.
4. Is 32 a multiple of 6?
5. Is 81 a multiple of 9?
6. Is 98 a multiple of 7? Is
7. Is 24 a multiple of 7?
8. 70 a multiple of 5? Is
9. Is 37 a multiple of 6?
10. 64 a multiple of 9?
Grade 4 • Chapter 8 Fractions
11. Is 45 a multiple of 9?
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