Prime or Composite
Is 17 Prime or Composite?
Give proof if it is composite.
Prime.
It has exactly 2 factors. 1, 17
What is the prime factorization of 6?
PF = 2x3
Find the GCF and LCM of 15 and 6. Use a Venn Diagram to show shared and unique prime factors. Show all work.
GCF = 3
LCM = 2x3x5 = 30
(2(3)5)
Find the GCF of 36 and 20.
2 L 36. 20
2 L 18 10
9 5
GCF = 2x2=4
Steve has 40 red and 16 blue marbles. What is the greatest number of bags he can fill with equal amounts of each color marble?
GCF - He can make 5 bags.
Is 21 Prime or Composite?
Give proof if it is composite.
Composite.
It has 4 factors. Give at least 3: 1, 21, 3, 7.
What is the prime factorization of 12?
Use exponents to simplify.
PF = 2x2x3 or 22x3
Find the GCF and LCM of 12 and 20. Use a Venn Diagram to show shared and unique prime factors. Show all work.
GCF = 2x2 = 4
LCM = 3x2x2x5 = 60
VD: (3(2,2)5)
Find the LCM of 8 and 12.
4 L 8 12
2 3
LCM = 4x2x3 = 24
Sherry has to empty the paper shredder in her office once every 6 days. She needs to empty the recycling bin every 4 days. If she emptys both today, in how many days will she need to do both again on the same day?
LCM - Sherry will need to empty both in 12 days.
Is 29 prime or composite?
Give proof if it is composite.
Prime.
It has exactly 2 factors. 1, 29
What is the prime factorization of 36?
PF = 2x2x3x3 = 22x32
Find the GCF and LCM of 8 and 24. Use a Venn Diagram to show shared and unique prime factors. Show all work.
GCF = 2x2x2 = 8
LCM = 2x2x2x3 = 24
VD = (__(2,2,2)3)
Find the GCF of 48 and 30.
2 L 48 30
3 L 24 15
8 5
GCF = 2x3 = 6
Steve is having a cookout. He can buy buns in packs of 10. He can buy burgers in packs of 6. He needs equal amounts of burgers and buns so that he doesn't waste any food. How many should he buy?
LCM - Steve should buy 30 burgers and 30 buns. (3 packs of buns and 5 packs of burgers)
Is 184 Prime or Composite?
Give proof if it is composite.
Composite. It has at least 3 factors.
1, 184, 2 (because it is even.
What is the prime factorization of 60?
PF = 2x2x3x5 = 22x3x5
Find the GCF and LCM of 16 and 24. Use a Venn Diagram to show shared and unique prime factors. Show all work.
GCF = 2x2x2 = 8
LCM = 2x2x2x2x3 = 48
VD: (2(2,2,2)3)
Fid the LCM of 18 and 27.
3 L 18 27
3 L 6 9
2 3
LCM = 3x3x2x3 = 54
Vinny makes antipasto salad for his deli. He has a jar of 40 olives and a jar of 28 pepperoncini. He likes to put an equal number of each in his salads. What is the most number of salads he can make?
GCF - Vinny can make 4 salads.
Is 51 Prime or composite?
Give proof if it is composite.
Composite. It has at least 3 factors.
Proof: 1, 51, and 3 (5+1 is 6, 3 goes into 6)
What is the prime factorization of 144?
Simplify with exponents.
PF = 2x2x3x2x2x3 = 24x32
Find the GCF and LCM of 8 and 13. Use a Venn Diagram to show shared and unique prime factors. Show all work.
GCF = 1
LCM = 2x2x2x13 = 104
VD = (2,2,2(__)13)
Find the GCF and LCM of 48 and 32.
4 L 48 32
4 L 12 8
3 2
GCF = 4x4 = 16
LCM = 4x4x3x2 = 96
Sarah is coding a robot for her technology class. She codes it to blink yellow every 6 seconds and blink blue every 14 seconds. The robot is coded to blink green every time it blinks yellow and blue at the same time. How often will the robot blink green?
LCM - The robot will blink green every 42 seconds.