Download Expressions and Fractions Prime Factorization

Expressions and Fractions
Prime Factorization
1. The GCF (Greatest Common Factor) of 50 and 200 is:
(A) 15
(B) 50
(C) 4
(D) 20
Solution:
The factors of 50 = 2*5*5
The factors of 200 = 2*2*2*5*5
The GCF (Greatest Common Factor) of 50 and 200 = 2*5*5 = 50
2. The GCF of 18ab2 and 72a2b is:
(A) 18a
(B) 9ab
(C) 12ab
(D) 18ab
Solution:
18ab 2 = 2 × 3 × 3 × a × b × b
72a 2 b = 2 × 2 × 2 × 3 × 3 × a × a × b
GCF = 2 × 3 × 3 × a × b
GCF = 18ab
3. The GCF (Greatest Common Factor) of the number 10 and 26 is:
(A) 130
(B) 65
(C) 2
(D) None of the above is correct
Solution:
10 = 5 × 2
26 = 13 × 2
GCF = 2
4. The GCF (Greatest Common Factor) of the number 32x4 and 16x is:
(A) 16x
(B) 32x
(C) 32x4
(D) 64x3
Solution:
32x 4 = 2 × 2 × 2 × 2 × 2 × x × x × x × x
16x = 2 × 2 × 2 × 2 × x
GCF = 2 × 2 × 2 × 2 × x
GCF = 16x
5. Find the factors of 63:
(A) 1, 2, 7, 63
(B) 1, 3, 9, 21
(C) 1, 3, 7, 42
(D) 1, 3, 7, 9, 21and 63
Solution:
A factor is a whole number that divides another whole number without
leaving any remainder
63 when divided by 1, 3, 7, 9, 21and 63 leaves no remainder
So the factors of 63 are 1, 3, 7, 9, 21and 63
6. Choose in the correct option: 19 is a _________ number.
(A) Prime
(B) Composite
(C) Complex
(D) Irrational
Solution:
A composite number is a whole number greater than one that has more than
two factors.
A prime number is whole number with exactly two factors: 1 and the number
itself.
The factors of 19 are 1, 19.
Therefore, 19 is a prime number.
7. Find the GCF of 30, 16 and 18.
(A) 5
(B) 3
(C) 2
(D) 0
Solution:
30 = 2 × 3 × 5
16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3
GCF = 2
=2
8. What is the GCF of 40 and 90?
(A) 60
(B) 10
(C) 20
(D) 600
Solution:
40 = 2 × 2 × 2 × 5
90 = 2 × 3 × 3 × 5
GCF = 2 × 5
GCF = 10
9. The GCF of 45 and 18 is:
(A) 19
(B) 9
(C) 17
(D) 18
Solution:
45 = 3 × 3 × 5
18 = 2 × 3 × 3
GCF = 9
10. The GCF of 15, 25 and 35 is:
(A) 25
(B) 22
(C) 5
(D) 55
Solution:
15 = 3 × 5
25 = 5 × 5
35 = 5 × 7
GCF = 5
11. Two football teams are marching at an event. There are 32 members in
one team and 40 in the other. They are marching in rows of equal size that
are as wide as possible. How many people are in each row?
(A) 16
(B) 8
(C) 24
(D) 28
Solution:
The maximum number of people in each row is the G.C.F. of the number of
members in each team.
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
GCF = 2 × 2 × 2
GCF = 8
12. Select the correct word.77 is a _________ number.
(A) Prime
(B) Composite
(C) Complex
(D) None of the above
Solution:
A composite number is a whole number greater than one that has more than
two factors.
A prime number is whole number with exactly two factors: 1 and the number
itself.
The factors of 77 are 1, 7 and 11.
Therefore, 77 are a composite number.
13. Find the GCF of 625 and 225:
(A) 25
(B) 65
(C) 55
(D) 26
Solution:
625 = 5 × 5 × 5 × 5
225 = 3 × 3 × 5 × 5
GCF = 5 × 5
GCF = 25
14. Two boxes contain balls. The first has 36 red balls, where as the second
box has 60 yellow balls. They are to be, arranged in rows of equal width.
How wide is the widest row possible?
(A) 15
(B) 30
(C) 12
(D) 36
Solution:
The widest row formed is the GCF of the number of each type of ball.
36 = 2 × 2 × 3 × 3
60 = 2 × 2 × 3 × 5
GCF = 2 × 2 × 3
GCF = 12
15. Find two prime numbers; with sum equal to or less than five, whose GCF
is one.
(A) 2 and 4
(B) 2 and 3
(C) 3 and 4
(D) 3 and 5
Solution:
2 and 3 are the two prime numbers: with sum equal to five whose GCF is 1
2 = 1× 2
3 = 1× 3
GCF = 1