Download Prime Factorization (SI)

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Generation Date: 04/14/2010
Generated By: Tamara Seymore
Prime Factorization
1. What is the greatest common factor (GCF) of 32, 40, and 56?
A. 16
B. 4
C. 6
D. 8
Pretest - Math
2. Study the bar graph below. Use it to answer the following question.
If a circle graph is used to display this same data, what percent of the circle graph
would represent basketball and soccer?
A. 36%
B. 24%
C. 12%
D. 40%
Prime Factorization
3. What is the least common multiple (LCM) of 10, 36, and 60?
A. 360
B. 180
C. 540
D. 60
Pretest - Math
4. How is the following number written in standard form?
5.79 × 104
A. 579,000
B. 57,900,000
C. 57,900
D. 57.9
Prime Factorization
5. What is the least common multiple (LCM) of 7, 6, and 14?
A. 126
B. 14
C. 84
D. 42
Pretest - Math
6. Maria went to the grocery store and bought 36 quarts of milk. How many gallons of
milk did she buy?
A. 18 gallons
B. 14 gallons
C. 9 gallons
D. 6 gallons
Prime Factorization
7. What is the greatest common factor (GCF) of 112, 140, and 168?
A. 14
B. 28
C. 32
D. 56
Pretest - Math
8. Janelle cut out and pasted together copies of the pattern pieces below.
What three-dimensional figure could be formed?
A. hexagonal pyramid
B. pentagonal pyramid
C. triangular pyramid
D. rectangular prism
Prime Factorization
9. What is the greatest common factor (GCF) of 20 and 28?
A. 2
B. 7
C. 12
D. 4
Pretest - Math
10. The current temperature of 13°F below zero is 27°F below the high temperature of
the day. What is the high temperature for the day?
A. 16°F
B. 14°F
C. 40°F
D. -40°F
Answers
1. D
2. B
3. B
4. C
5. D
6. C
7. B
8. A
9. D
10. B
Explanations
1. Start by factoring each number completely.
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
56 = 2 × 2 × 2 × 7
The factors highlighted in red are common to all three factorizations. Therefore, 2 × 2 ×
2 = 8 is the GCF.
3. Start by factoring each number completely.
10 = 2 × 5
36 = 2 × 2 × 3 × 3
60 = 2 × 2 × 3 × 5
Now write each number in exponential form.
10 = 21 × 51
36 = 22 × 32
60 = 22 × 31 × 51
Since we are looking for the smallest multiple common to all three of the given numbers,
multiply together the largest power of each prime shown.
The largest power of 2 shown is 22.
The largest power of 3 shown is 32.
The largest power of 5 shown is 51.
So, the least common multiple is 22 × 32 × 51 = 180.
5. Start by factoring each number completely.
7=7
6=2×3
14 = 2 × 7
Now write each number in exponential form.
7 = 71
6 = 21 × 3 1
14 = 21 × 71
Since we are looking for the smallest multiple common to all three of the given numbers,
multiply together the largest power of each prime shown.
The largest power of 2 shown is 21.
The largest power of 3 shown is 31.
The largest power of 7 shown is 71.
So, the least common multiple is 21 × 31 × 71 = 42.
7. Start by factoring each number completely.
112 = 2 × 2 × 2 × 2 x 7
140 = 2 × 2 × 5 × 7
168 = 2 × 2 × 2 × 3 × 7
The factors highlighted in red are common to all three factorizations. Therefore, 2 × 2 ×
7 = 28 is the GCF.
9. 20 can be factored into 5 × 4.
28 can be factored into 7 × 4.
Therefore, 4 is the GCF.
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