Lesson Two: Prime Factors Math Worksheet With Answers Page 2
ADVERTISEMENT
1
2
3we can see that
gcd ( ��, �� ) = ��
∗ ��
∗ ��
∗ … ∗ ��
min (��
,��
)
min (��
,��
)
min (��
,��
)
min (��
,��
)
1
1
2
2
3
3
��
��
��
1
2
3
lcm ( ��, �� ) = ��
∗ ��
∗ ��
∗ … ∗ ��
max (��
,��
)
max (��
,��
)
max (��
,��
)
max (��
,��
)
1
1
2
2
3
3
��
��
��
1
2
3
Don’t let the notation intimidate you; understanding the concepts at work here is
more important. Note that some of ��
of ��
may be 0 for some of the primes.
��
��
4) Aaron teaches at a school where class sizes range from 15 to 30. One day, he decides
that he wants to arrange his students’ desks in a rectangular array and notices that
he can only do so with one long row of desks. What is the sum of all possible values
for the number of students in his class?
Since he can only have one row, this means he has a prime number of students. The
primes between 15 and 30 are 17, 19, 23, and 29. Thus, our answer is
17+19+23+29 = 88.
5) Consider the number 100.
a) How many factors does it have?
b) What is the sum of those factors?
c) What is the product of those factors?
As before, we find the prime factorization to be 2
∗ 5
.
2
2
a) A divisor of 100 must be in the form with 2
∗ 5
, with ��, �� = 0,1,2. We can
��
��
summarize our factors with a chart:
a\b
0
1
2
0
2
∗ 5
= 1
2
∗ 5
= 5
2
∗ 5
= 25
0
0
0
1
0
2
1
2
∗ 5
= 2
2
∗ 5
= 10
2
∗ 5
= 50
1
0
1
1
1
2
2
2
∗ 5
= 4
2
∗ 5
= 20
2
∗ 5
= 100
2
0
2
1
2
2
Verify that these are all the factors. We have 3 ∗ 3 = 9 factors. Consider, in general,
�� = ��
∗ ��
∗ ��
∗ … ∗ ��
.
��
��
��
��
1
2
3
��
��
1
2
3
The prime factorization of a includes anywhere from 0 to ��
powers of ��
, giving
1
1
��
+ 1 choices for the exponent of ��
. Proceeding similarly for the rest of the primes,
1
1
we have that the total number of divisors of �� to be
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education