Divisibility
Check if 324 is divisible by 2, 3, and 6.
324 is divisible by 2, 3, and 6.
Find the LCM for 7 and 21.
LCM = 42
7: 7, 14, 21, 28, 35, 42, 49, 56
21: 21, 42, 63, 84, 105
Find the GCF for 40 and 45.
GCF = 5
40 45
1 40 1 45
2 20 3 15
4 10 5 9
5 8
Use prime factorization: 64
64
8 8
2 4 2 4
2 2 2 2
26
Sanjana is baking cupcakes. The cake recipe makes 10 cupcakes, and the icing recipe makes 8. What is the smallest number of iced cupcakes can she make, without having any leftovers?
10: 10, 20, 30, 40, 50, 60
8: 8, 16, 24, 32, 40, 48
Check if 185 is divisible by 3, 4, and 5.
185 is divisible by 5 only.
Find the LCM for 10 and 12.
LCM = 60
10: 10, 20, 30, 40, 50, 60, 70, 80
12: 12, 24, 36, 48, 60, 72, 84
Find the GCF for 8 and 20.
GCF = 4
8 20
1 8 1 20
2 4 2 10
4 5
Use prime factorization for: 24
24
2 12
2 6
2 3
23 x 3
There are 120 purple marbles and 80 red marbles. I want to put them in equal rows, with only 1 colour in each row. What is the greatest number of marbles I can put in each row?
This is a GCF problem. GCF = 40
120 80
1 120 1 80
2 60 2 40
3 40 4 20
4 30 5 18
5 24 8 10
6 20
10 12
Check if 279 is divisible by 3, 6, and 9.
279 is divisible by 3 and 9, but not 6.
Find the LCM for 8 and 14.
LCM = 56
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
14: 14, 28, 42, 56, 70, 84, 98
Find the GCF for 70 and 90.
GCF = 10
70 90
1 70 1 90
2 35 2 45
5 14 3 30
7 10 5 18
6 15
9 10
Use prime factorization for 80
80
2 40
4 10
2 2 2 5
24 x 5
Tim Hortons sells boxes of timbits with 10 per box. They sell muffins with 6 per box. I want an equal number of timbits and muffins. What is the smallest amount of each I can order? How many boxes of timbits do I need? How many boxes of muffins?
This is an LCM problem. LCM = 30
6: 6, 12, 18, 24, 30, 36, 42
10: 10, 20, 30, 40, 50, 60, 70
I need 5 boxes of timbits and 3 boxes of muffins.
Check if 58, 125 is divisible by 3, 4, and 5.
58, 125 is divisible by 3 and 5, but not 4.
Find the LCM for 6 and 9.
LCM = 18
6: 6, 12, 18, 24, 30, 36
9: 9, 18, 27, 36, 45, 54
Find the GCF for 100 and 60.
GCF = 20
100 60
1 100 1 60
2 50 2 30
4 25 3 20
5 20 4 15
10 10 5 12
6 10
Use prime factorization for 75
75
3 25
5 5
3 x 52
I have 30 photos that are 4" x 6" and 54 photos that are 5" by 7." I am organizing them into scrap books, and I want the same number of photos on each page. I also want each page to only have one size of photos. What is the greatest number of photos I could have on each page?
This is a GCF problem. GCF = 6
30 54
1 30 1 54
2 15 2 27
3 10 3 18
5 6 6 9
Check if 444 is divisible by 3, 4, and 6.
444 is divisible by 3, 4, and 6.
Find the LCM for 25 and 20.
LCM = 100
25: 25, 50, 75, 100, 125
20: 20, 40, 60, 80, 100, 120
Find the GCF for 56 and 72.
GCF = 8
56 72
1 56 1 72
2 28 2 36
4 14 3 24
7 8 4 18
6 12
8 9
Use prime factorization for 100.
100
10 10
2 5 2 5
22 x 52
Tubs of ice cream contain 42 scoops each. 1 package of waffle cones has 14 cones. What is the smallest number I can buy of each, so that I will not have leftovers?
This is a LCM problem. LCM = 42
14: 14, 28, 42, 56
42: 42, 84