Download Family Letter 2

CHAPTER
2
Family Letter
Section B
What We Are Learning
Dear Family,
Factors and Multiples
Your child will be learning divisibility rules. Finding the prime
factorization of a number is one way to find its prime factors.
A prime number is a special number that only has two factors,
1 and itself.
Vocabulary
These are the math words
we are learning:
composite number
a whole number that has
more than two factors
greatest common factor
(GCF) the greatest whole
number that divides evenly
into each number in a
group
Your child will learn to find the prime factorization of a number
by using a factor tree and a step diagram. This is how your
child will use a factor tree to find the prime factors of a
composite number.
Use a factor tree to find the prime factorization of 84.
84
7 • 12
Write 84 as a product of two factors.
7•3•4
least common multiple
(LCM) the common
multiple with the least
value
7•3•2 •2
multiple the product of
that number and a whole
number
The prime factorization of 84 is 7 • 3 • 2 • 2.
Using exponents, this is written as 22 • 3 • 7.
prime factorization
when a composite number
is written as a product of
its prime factors
prime number a whole
number that is greater
than one and has exactly
two factors
Continue factoring until all the numbers
are prime.
This is how your child will use a step diagram to find the prime
factors of a composite number.
Use a step diagram to find the prime factorization
of 242.
Divide the number by the smallest prime
number possible
121 is not divisible by 2, so go to the next
prime number that will divide evenly into
121.
Divide 11 by 11.
2 242
11 121
11 11
1
The quotient is 1
The prime factorization of 242 is 112 • 2.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
13
Holt Mathematics
CHAPTER
2
Family Letter
Section B, continued
Prime factorization is very helpful when reducing fractions to
lowest terms. Your child will also use prime factorization to find
the greatest common factor (GCF) and the least common
multiple (LCM) of two or more given numbers.
To determine the GCF, your child will list all the factors of each
given number and then circle the greatest number that each list
has in common. Another method your child will learn is to list
the prime factors of each given number, circle the matching
factors, then find the product of these common factors.
Find the greatest common factor of 24 and 40.
24 2 • 2 • 2 • 3
40 2 • 2 • 2 • 5
Write the prime factorization for each
number and circle the matching factors.
2•2•28
Multiply the common factors.
The GCF is 8.
The factors of a number are those numbers that form the
product. The multiple of a number is the product of that
number and another whole number.
For example, the multiples of 8 are 8, 16, 24, 32, ...
Your child will find the least common multiple by listing all the
multiples of each number or by finding the prime factorization
of each number and multiplying the factors in each list. If some
of the factors are repeated, your child should only multiply
those factors once.
Find the least common multiple (LCM) of 15 and 35.
15 3 • 5
35 7 • 5
3 • 7 • 5 105
Write the prime factorization of each
number.
List the factors of both numbers, using
the circled factors only once.
Multiply the factors in the list.
The LCM is 105.
The skills and concepts your child will learn in this section will
help your child as he or she begins to work with fractions and
more complex numbers. Review basic multiplication and
division facts to help your child recognize simple factors.
Sincerely,
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
14
Holt Mathematics
Name
CHAPTER
2
Date
Class
Family Letter
Factors and Multiples
Use a factor tree to find the prime factorization.
1. 88
2. 376
3. 425
Use a step diagram to find the prime factorization.
4. 168
5. 405
6. 880
Find the greatest common factor (GCF).
7. 12, 28
8. 36, 45
9. 36, 48, 108
10. 14, 42, 56
11. 70, 105
12. 38, 57
13. 22, 55, 110
14. 8, 36, 72
Find the least common multiple (LCM).
15. 8, 12
16. 18, 24
17. 6, 15
18. 2, 3, 4
19. 6, 9, 12
20. 4, 10, 20
21. 5, 6, 9
22. 2, 5, 7
Answers: 1. 23 • 11 2. 23 • 47 3. 52 • 17 4. 23 • 3 • 7 5. 34 • 5 6. 24 • 5 • 11 7. 4 8. 9 9. 12 10. 14 11. 35
12. 19 13. 11 14. 4 15. 24 16. 72 17. 30 18. 12 19. 36 20. 20 21. 90 22. 70
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
15
Holt Mathematics
Name
Date
CHAPTER
2
Class
Family Fun
Multiple Mania
Materials
2 number cubes for each player
2 game markers
Directions
• Players take turns rolling a pair of number cubes. Use the face value if
the cube comes up 2, 3, 4, 5, or 6, but use 9 if a 1 is rolled. If you roll
double 6’s, you can cover any number on the board.
• Find the Least Common Multiple for the numbers that were rolled.
• Place a marker on that number on the game board. If all instances of the
least common multiple are already covered, then you lose your turn.
• The game is over when one player has 4 markers in a row horizontally,
vertically, or diagonally.
36
45
8
45
20
35
18
36
20
12
6
10
12
4
25
18
45
15
15
9
10
36
9
4
8
12
20
25
30
15
10
12
30
9
15
8
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
16
Holt Mathematics