Download Unit 4 Test Factors, Multiples and Prime Numbers Name: Class

Unit 4 Test
Factors, Multiples and Prime Numbers
ANSWERS
Name: ____________________________
Green
/20
Blue
/16
Black
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Class: _______
Green
/20
List the factors for the following numbers (1 mark each)
1) 36
2) 84
1, 2, 3, 4, 6, 9, 12, 18, and 36
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
List the first 5 multiples of the following. (1 mark each)
3) 12
4) 19
12, 24, 36, 48, 60
19, 38, 57, 76, 95
List the factors of each set of numbers and circle the common factors. (2 marks each)
5) 72 and 96
6) 102 and 135
72: 1, 2, 3, 4, 6, 7, 8, 12, 18, 24, 36, 72
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
102: 1, 2, 3, 6, 17, 34, 51, 102
135: 1, 3, 5, 9, 15, 27, 45, 135
List the first four (4) common multiples of the following sets of numbers. (2 marks each).
7) 6 and 9
8) 8 and 12
18, 36, 54, 72
24, 48, 72, 96
9) Circle the four prime numbers. (2 marks)
9 19 27 33 37 43 51 67
Draw factor trees and write each number as a product of its primes (2 marks each)
10) 40
23 x 5
11) 90
2 x 32 x 5
12) 120
23 x 3 x 5
Blue
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Use prime factorization to find the GCF and LCM of the following sets of numbers. (3 marks each)
working out (1 mark)
GCF (1 mark)
1) 495 and 660
LCM (1 mark)
2) 684 and 912
GCF = 3 x 5 x 11 = 165
GCF = 22 x 3 x 19 = 228
LCM = 22 x 32 x 5 x 11 = 1980
LCM = 24 x 32 x 19 = 2736
Find 2 numbers that have a… (2 marks each)
3) LCM of 72 and a sum of 42
18 and 24
4) HCF of 12 and a sum of 96
36 and 60 or 12 and 84
5) Ken, Clea and Kristine are on the ISB Swim Team. They have the option of going to any of
the practices afterschool. Ken swims every other day, Clea swims every 3rd day and Kristine
swims every 4th day. If they all swam after school on Monday, after how many days will they
all swim at the same time? What day of the week will that be? (3 marks)
LCM of 2, 3 and 4 = 12 (1 mark)
12 Days later (1 mark)
Wednesday (1 mark)
6) An odd number between 90 and 110 has exactly three different prime factors. What’s the
number, explain your reasoning. (3 marks)
105 (1 mark)
divisible by 3, 5, and 7 (1 mark)
show their work (1 mark)
Black
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Question 1
Two bicycle wheels are different sizes and have
arrows drawn on them. When you ride the bicycle,
the arrows point in exactly the same direction
every 3.5 meters. One wheel has a circumference
that is 20 cm smaller than the other. What is the
exact circumference of each one? (4 marks)
LCM of C(small wheel) + C(big wheel) = 3.5 m = 350 cm
C(small wheel) + 20 cm = C(big wheel)
C(small wheel) = 50 cm
C(big wheel) = 70 cm
Question 2
Katherine is having a party. She has enough pizza and drinks so that everyone gets 3 slices of pizza
and 2 drinks without having any leftovers. If each whole pizza has 8 slices and drinks are sold in
boxes of 24 – how many people are at her party? (4 marks)
LCM of 2, 3, 8 and 24
24 people at the party
24 people x 3 slices each = 72 slices of pizza
72 slices of pizza / 8 slices per pizza = 9 pizzas
24 people x 2 drinks = 48 drinks = 2 boxes of drinks
Question 3
It takes the earth 1 year to orbit the sun. In that time, Mercury completes only 0.25 of an orbit,
and Venus 0.6 of an orbit. If all three planets are lined up as shown, how many years will it be until
they are lined up like this again? (4 marks)
SUN
M
V
E
Earth
Mercury
Venus
1
0.25
0.6
2
0.5
1.2
Looking to find the LCM of4 and 5 b/c
3
0.75
1.8
that is when there are full rotations of the
4
1.0
2.4
earth and other planets
5
1.25
3.0
LCM of 4 and 5 is 20