# Math 211 Chapter 5 Worksheet

1. Find the greatest common factor using the sets of factors: gcf(75,144).

2. Find the greatest common factor by repeatedly dividing prime numbers: gcf(105,132)

3. Find the greatest common factor by first finding prime factorization of each number: gcf(630,1848)

4. Find the greatest common factor by using the Euclidean Algorithm: gcf(957,3366)

5.a. Find gcf(a,b) if a is a multiple of b .

b. Find gcf(a,b) if a is a factor of b.

c. Find gcf(a,b) if a and b have no common factors .

6. a. Find two numbers such that their gcf is 7.

b. Can both, just one, or neither of the numbers be even ? Why?

c. Find two numbers , both greater than 100, such that their gcf is 7.

7. If p, q and r are distinct prime numbers, find
gcf(pqr,p^{2}r).

8. Let . If m divides n , what can you conclude about the prime factorization of m?

9. The numbers 2, 5, and 9 are factors of my locker number and there are 12 factors in all. What is my locker number and why?

Least Common Multiple

1. Find the least common multiple using the sets of factors: lcm(30,75).

2. Find the least common multiple by first finding prime factorization of each number: lcm(45,54)

3. Find the gcf if lcm (a,b)=b

4. Find the lcm if gcf (a,b)=a

5. Find two numbers whose lcm is 100.

6. What is the lcm(a,b) if the gcf(a,b)=1?

7. Write ≤, <, ≥, >, =, or ? in the following blanks. Use
? if the answer cannot be determined from the information given.

8. If lcm(a,b)=gcf(a,b), what do you know about the relationship between a and b? Why?

Fill in the following table.

Problem # | a | b | gcf(a,b) | lcm(a,b) |

9 | 3 | 4 | ||

10 | 20 | 12 | ||

11 | 32 | 38 | ||

12 | 16 | 15 | ||

13 | 10 | 14 |

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