Number Theory Applications
Would you use divisibility rules, prime and composite numbers, greatest common factor, least
common multiple, or square numbers to solve the following problems? After you decide, write which
concept is being used and then solve the problem.
1. Describe how you can tell if a number is a multiple of the following numbers: 2, 3, 4, 5, 6, 9,
and 10.
Concept used: ____________________________________
Solution:
2. a.
b.
c.
d.
List the first 10 square numbers
Give all the factors for the square numbers above.
Which of the square numbers have only 3 factors?
If you continued your list, what would be the next square number with only 3 factors?
Concept used: ____________________________________
Solution:
Concept used: ____________________________________
3. Find the prime factorization of 24 and 18. Put the factors into the Venn diagram. How
could the Venn diagram help you find the GCF and LCM?
Solution:
24
18
24
18
4. A U.S. president is elected every 4 years. A U.S. senator is elected every 6 years. If a senator
is elected the same year as the President, how many years will it be until the senator run for
re-election during a presidential campaign?
Concept used: ____________________________________
Solution:
5. Would you prefer your teacher to assign the odd-numbered problems or the prime numbered
problems for homework? Explain your answer.
Concept used: ____________________________________
Solution:
6. The Blue Line bus arrives at Summit Middle School every 20 minutes. The Express Shuttle
arrives at SMS every 3 minutes. How often do both busses arrive at the same time?
Concept used: ____________________________________
Solution:
7. 48 baseball cards and 72 football cards are to be shared equally among a group of scouts.
What is the greatest number of scouts in the troop for this to occur?
Concept used: ____________________________________
Solution:
8. Find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) for each pair
of numbers.
Solution:
a) 24 and 36
b) 12 and 24
c) 27 and 81
9. List all of the factor pairs for the following numbers.
Solution:
a. 36
b. 100
10. List the first 10 multiples of the following numbers.
Solution:
a. 12
b. 25