Prime & Composite
Is 47 a prime or composite number? Explain how you know.
Prime. Its only factors are 1 and 47.
What is the prime factorization of 72? Express your answer using exponents.
72
6 12
2 3 3 4
2 2
prime factorization of 72 = 2^3 xx 3^2
Find the GCF of 36 and 54
Prime factorization of 36 = 2^2 xx 3^2
Prime factorization of 54 = 2 xx 3^3
GCF = 2 xx 3^2 = 18
Liana has 30 mint chocolates and 45 caramel chocolates. They want to divide them into gift bags so that each bag has the same number of each type of chocolate with none left over. What is the greatest number of bags Liana can make?
The greatest number of bags Liana can make is 15.
(The GCF of 30 and 45 = 15)
Catherine waters her houseplant every 4 days and trims it every 14 days. If she did both today, in how many days will she next water and trim her plant on the same day?
Catherine will next water and trim her plant on the same day in 28 days.
(The LCM of 4 and 14 is 28)
Without performing any division, explain why 4, 125, 930 is a composite number. Name at least three factors besides 1 and itself.
It is composite because it ends in a 0.
Additional factors include 2 (even number), 5 (ends in a 0), 10 (ends in a zero) and 3 (the sum of its digits = 4+1+2+5+9+3+0 = 24 is divisible by 3).
Determine the missing prime factor in this equation:
90 = 2 xx 3^2 xx
5
2 xx 3^2 = 2 xx 9 = 18
18 xx 5 = 90
Find the LCM of 12 and 18
Prime factorization of 12 = 2^2 xx 3
Prime factorization of 18 = 2 xx 3^2
LCM = 2^2 xx 3^2 = 36
The 63 Ossington and 127 Davenport buses both stop at the corner of Ossington and Davenport. The 63 arrives at the stop every 15 minutes. The 127 arrives at the stop every 20 minutes. If both buses just left the stop at the same time, in how many minutes will they next arrive at the stop at the exact same time?
The 63 and 127 will next arrive at the Ossington and Davenport stop at the exact same time in 60 minutes (or 1 hour).
(The LCM of 15 and 20 = 60)
Referring back to Liana's gift bags from World Problems I (30 mint chocolates and 45 caramel chocolates split into 15 bags), how many mint chocolates and caramel chocolates will be in each individual bag?
Each of Liana's gift bags will contain 2 mint chocolates and 3 caramel chocolates.
(30 / 15 = 2 and 45 / 15 = 3)
Without using long division, determin whether 3, 513, 294 is a prime or composite number. If composite, name at least three factors of this number other than 1 and itself and state the divisibility rule you used for each.
Composite
Factors identified using divisibility rules include...
2 (the last digit is even)
3 (the sum of the digits 3+5+1+3+2+9+4 = 27 is divisible by 3)
6 (the number is divisible by 2 and 3)
9 (the sum of the digits = 27 is divisible by 3)
Determine the number whose prime factorization is the product of the square of the smallest prime number and the cube of the second smallest prime number.
2^2 xx 3^3 = 4 xx 27 = 108
Using prime factorization, find the GCF and LCM of 45 and 105.
Prime factorization of 45 = 3^2 xx 5
Prime factorization of 105 = 3 xx 5 xx 7
GCF = 3 xx 5 = 15
LCM = 3^2 xx 5 xx 7 = 315
The mural club students are creating banners for spirit week. They have two pieces of banner fabric measuring 120 cm and 150 cm long. They want to cut both pieces into ribbons of equal length without wasting any fabric. What is the longest length each ribbon can be?
The longest length each ribbon can be is 30 cm.
(The GCF of 120 and 150 = 30)
Finn spent $4.50 on sport drinks. Rafay spent $6.00 on the exact same sports drinks at the same price per bottle.
a) What is the maximum possible price for a single bottle of sports drink?
b) How many bottles did Finn buy?
c) How many bottles did Rafay buy?
The maximum price for a single bottle of sports drink is $1.50 (or 150 cents).
(The GCF of 450 and 600 = 150)
Finn bought 3 bottles and Rafay bought 4 bottles.
(450 / 150 = 3 and 600 / 150 = 4)
Identify if 91 is prime or composite. If composite, list all of its factors using a factor rainbow or factor tower.
Composite
91
1 91
7 13
Determine the prime factorization of 588 using a factor tree.
588
2 294
2 147
3 49
7 7
prime factorization of 588 = 2^2 xx 3 xx 7^2
Given the numbers 60 and 90, identify two other common factos besides their GCF and two other common multiples besides their LCM.
GCF of 60 and 90 = 30. Other common factors: 2, 3, 5, 6, 10, 15
LCM of 60 and 90 = 180. Other common multiples: 360, 540, 720, etc.
Winona has purchased two Halloween-themed disco balls for the first school dance of the year. One has purple-blinking lights and the other has green-blinking lights. Both blink at fixed intervals. The purple lights blink every 36 seconds and the green lights blink every 48 seconds. If the lights are turned on at the same time, how many minutes and seconds will pass before the purple and green lights blink at the exact same instant? (ooooo spooky!!)
The purple and green lights will blink at the exact same instant after 2 minutes and 24 seconds.
(The LCM of 36 and 48 is 144. 144 sec = 2 min 24 sec)
Two busses are taking all the students at Winona SPS downtown to a special Youth Career Pathways Fair. Bus A's driver is much more street savvy and can make the round trip downtown and back to the school to pick up the next load of kids in 25 minutes. Bus B's driver isn't as great, and it takes them 40 minutes to make the round trip. If both buses depart from the school at 8:00am with their first load of students, at what time will they next depart the school at the same time?
The next time Bus A and Bus B will depart the school at the same time will be at 11:20am.
(LCM of 25 and 40 = 200 minutes = 3 hrs, 20 min after 8am --> 11:20am)
A rectangular rug measures 19 ft by 13 ft. Withou calculating the total area of the rug, explain whether the area of the rug is a prime or composite number.
The area of the rug is a composite number. The dimmensions of the rug (19 and 13) serve as factors of the area, because the area of a rectangle = length x width. Since the area has at least one factor pair (19 and 13) besides 1 and itself, it must be composite.
What is the number whose prime factorization is eual to the smallest two-digit prime number cubed?
The smallest two-digit prime number is 11.
11^3 = 11 xx 11 xx 11 = 1,331
The GCF of two number is 14 and their LCM is 84. One of the numbers is 28, what is the other number?
42
Because Number A x Number B = GCF x LCM
28 x B = 14 x 84
28 x B = 1,176
B = 42
High school students on Wester Tech's Ambassadors Crew are making welcome kits to pass out to the middle schoolers coming to the Open House that evening. The Parent Council has given them 84 pens, 112 notebooks and 140 stickers for the kits.
a) What is the maximum number of identical kits the Ambassador Crew can assemble with no items left over?
b) How many notebooks will be in each kit?
The maximum number of kits the ambassador crew can assemble is 28 kits.
(The GCF of 84, 112 and 140 = 28)
Each kit will contain 4 notebooks.
(112 / 28 = 4)
Ms. Pothar and Ms. Boultbee are training on separate circular tracks. Ms. Pothar is training on a track that is 400 metres around and Ms. Boultbee is training on a track that is 700 metres around. If Ms. Pothar and Ms. Boultbee start at the start line at the same time and keep running at the same speed as one another, after how many total metres will they both return to the start line at the exact same moment?
Ms. Pothar and Ms. Boultbee will return to the start line at the exact same moment in 2,800 metres.
(LCM of 400 and 700 is 2,800)