Lesson Two: Prime Factors Math Worksheet With Answers Page 3
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1
2
3�� ( �� ) = ( ��
+ 1 ) ∗ ( ��
+ 1 ) ∗ ( ��
+ 1 ) … ∗ (��
+ 1).
1
2
3
��
b) Using our chart, our factors are 1, 2, 4, 5, 10, 20, 25, 50, 100. Note that we can pair up
the divisors as shown:
1
2
4
5
10
20
25
50
100
100
50
25
20
10
5
4
2
1
In each column, the top and bottom divisors multiply to 100. Thus, letting P be the
product of our numbers,
P
1 ∗ 2 ∗ 4 ∗ 5 ∗ 10 ∗ 20 ∗ 25 ∗ 50 ∗ 100
P
100 ∗ 50 ∗ 25 ∗ 20 ∗ 10 ∗ 5 ∗ 4 ∗ 2 ∗ 1
��
100 ∗ 100 ∗ 100 ∗ 100 ∗ 100 ∗ 100 ∗ 100 ∗ 100 ∗ 100
2
Note that there are �� ( 100 ) = 6 100′�� to be multiplied. Thus, ��
= 100
, or
2
6
�� = 100
.
6/2
Then, using the same method, in general, �� ( �� ) = ��
.
��(��)
2
c) Using our chart, the sum is 2
∗ 5
+ 2
∗ 5
+ 2
∗ 5
+ 2
∗ 5
+ 2
∗ 5
+ 2
∗
0
0
0
1
0
2
1
0
1
1
1
5
+ 2
∗ 5
+ 2
∗ 5
+ 2
∗ 5
. That doesn’t look like too much fun, so we factor:
2
2
0
2
1
2
2
( 5
) + 2
( 5
) + 2
( 5
) = ( 2
)( 5
2
+ 5
+ 5
+ 5
+ 5
+ 5
+ 5
+ 2
+ 2
+
0
0
1
2
1
0
1
2
2
0
1
2
0
1
2
0
) = 217. Try to find a general expression yourself!
5
+ 5
1
2
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