Name_____________________________________ Date______________________________ Period #_______
Study Guide for Prime Factorization, Common Multiples and Common Factors Test
Answer each question to the best of your ability. Remember to show all your work and circle your final answer.
1.
Alex wrote down his favorite numbers. (Worth 4 points)
The numbers are 1, 3, 11, 14, 15, 16, 17, 20, 23, 25, 29 and 31.
a. What are the prime numbers in Alex’s list?
b.What are the composite numbers in Alex’s list?
c.What are the even numbers in Alex’s list?
d.What are the perfect squares in Alex’s list?
2.
Place a check in the appropriate column for each number
3.
Alexa likes the number 36.
a. What are the distinct factors of 36?
b. Is 36 a perfect square? How do you know?
a.
b.
4.
4. A number is divisible by both 2 and 3. What other number must it be divisible by?
a. 4
b. 6
c. 9
d. 10
Answer
5.
What are the common factors of 36 and 24?
a. 1, 2, and 4
b. 1, 2, 3, 4, 6 and 8
c. 1, 2, 3, 4, 6 and 12
d. 1, 2, 3, 4, 6, 8, 12, 18, and 24
6.
What type of number has more than two factors?
a. a prime number
b. a composite number
c. the multiplicative identity
d. a factor pair
7.
16.
Which of the following is divisible by 9?
a. 24,571
b. 38,211
c. 42,381
d. 57,631
8.
Complete a factor tree for 128. Then, write the prime factorization using powers.
9.
Determine the greatest common factor for 42 and 84 using prime factorization.
10.
Identify the base and exponent in each power. Then, write each power in words and calculate its
value. (Worth 2 points)
a. 43
b. 26
11.
What is the least common multiple of 8, 10, and 12?
a. 120
b. 360
c. 670
d. 960
12.
What is a common multiple of 8 and 12?
a. 80
b. 144
c. 108
d. 248
13.
What is the greatest common factor of 26 and 104?
a. 2
b. 13
c. 26
d. 104
14.
What is the prime factorization of 76?
a. 2 x 38
b. 2 x 2 x 19
c. 2 x 3 x 18
d. 2 x 2 x 2 x 2 x 3
15.
What is the relationship between 13 and 39?
a. 13 is a multiple of 39
b. 39 is a multiple of 13
c. 13 is divisible by 39
d. 39 is a factor of 13
16.
What is the least common multiple of 6, 10, and 18?
a. 90
b. 120
c. 180
d. 360
17.
BONUS
Jennifer is making bouquets of flowers. She has 25 roses, 45 tulips, and 15 snapdragons.
She divides the flowers equally to make as many bouquets as possible. She uses up all the flowers.
What number of snapdragons are in each bouquet?
a. 3
b. 5
c. 9
d. 15