Factors and Multiples
Start with 8. Find all the multiples of 8 up to 100.
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
Identify whether each number is Prime or Composite:
a) 17
b) 27
c) 31
a) Prime b) Composite (3×9) c) Prime
The sequence below shows a number pattern. Use the rule "Add 8" to find the next two terms:
Term 1 Term 2 Term 3 Term 4 Term 5 2 8 16 ? ?
24, and 32.
Natalie and Ashley sell cupcakes for their school bake sale. Each week, they earn $15. Their goal is to earn at least $105 for their school, Which week will they have met their goal? Use the input-output method to find your answer.
Week 7 : 7x15=105
Ms. Lewis has chosen a mystery number. Her number is larger than 14 and smaller than 40 and it has exactly three factors. What could her number be?
The factors of 25 are 1, 5, and 25 (exactly three factors).
Antoni and Ashley are working as partners to find multiples of 4. Which of the following numbers are multiples of 4? Select all answers that apply.
A)24
B)14
C)28
D)32
E)36
A)24, C)28, D)32 and E)36
Jeremy sorted several numbers into the chart below:
Category A Category B Category C
5, 19, 31, 53 9, 25, 42, 63 1
Part A: How did Jeremy categorize the numbers in his chart?
Part B: Immanuel said that 51 belongs in Category A because it is an odd number, and all odd numbers are prime. Do you agree or disagree with Immanuel? Justify your thinking using factor pairs.
Part A: Category A = Prime numbers; Category B = Composite numbers; Category C = Neither prime nor composite (1).
Part B: Disagree with Immanuel. 51 is composite because its factor pairs are 1×51 and 3×17. Not all odd numbers are prime.
Johnny is working on a math problem for homework. Look at this numerical pattern and find the rule:
12, 18, 15, 21, 18, ?
What is the 6th number in the sequence?
The 6th number in the sequence is 24.
Rule :(Add 6 , subtract 3)
A 4th-grade class surveyed 30 students about their favorite after-school activity and organized the data into the bar graph below:
Based on the graph, which after-school activity is the most popular among the surveyed 4th graders, and how many students chose it?
Sports: 10 students
Reading: 4 students
Video Games: 8 students
Art/Crafts: 6 students
Outdoor Play: 2 students
Sports is the most popular activity, chosen by 10 students.
Ms. Martinez asked her 4th-grade class to analyze three numbers: 29, 39, and 51.
Which of the following correctly lists all factor pairs for each of the three numbers?
Tenzin and Shayla are working on a math worksheet. They must find the factor pairs for each of the following numbers: 18, 36, and 43.Based on their work, what are the factor pairs?
a) 18: (1×18),(2×9),(3×6)
b) 36: (1×36),(2×18),(3×12),(4×9),(6×6)
c) 43: (1×43)
Explain the relationship between factor pairs and whether a number is classified as prime or composite.
Prime numbers have exactly 1 factor pair (1 and itself). Composite numbers have more than 1 factor pair.
Estaban and Reema are working on a math problem together. Look at the numerical pattern below:
Estaban says: "The rule is add 6, then subtract 3."
Reema says: "The rule is multiply by 2, then subtract 6."
Which student is correct, and what is the 6th number in the sequence?
Estaban is correct. The 6th number in the sequence is 24.
The graph below compares the number of books read by Boys and Girls in grades 3, 4, and 5:
Grade 3: Boys = 15, Girls = 20
Grade 4: Boys = 25, Girls = 30
Grade 5: Boys = 20, Girls = 15
How many more total books were read by Grade 4 students compared to Grade 3 students?
20 more books
Explanation:
Grade 4 Total: 25 + 30 = 55 books
Grade 3 Total: 15 + 20 = 35 books
Difference: 55 - 35 = 20 books.
Luis is setting up a 24-hour gaming marathon live stream to raise money for his school. He wants to divide the 24 hours into gaming sessions of equal length so his friends can take turns playing.
If every session must be a whole number of hours with no breaks in between, what are all the different ways Luis can split up the 24 hours?
There are 8 different ways Luis can divide the marathon using equal shifts of 1, 2, 3, 4, 6, 8, 12, or 24 hours!
1 session of 24 hours (1x24=24)
2 sessions of 12 hours each (2x12=24)
3 sessions of 8 hours each (3x8=24)
4 sessions of 6 hours each (4x6 = 24)
6 sessions of 4 hours each (6x4 = 24)
8 sessions of 3 hours each (8x3 = 24)
12 sessions of 2 hours each (12x2 = 24)
24 sessions of 1 hour each (24x1 = 24)
Jose is working on an exit ticket problem for class. Which of the following is a true statement about prime and composite numbers?
A) The number 1 is a prime number because it only has one factor.
B) All odd numbers are prime numbers.
C) Every composite number has two or more factors.
D) 2 is a composite number because it is an even number.
C) Every composite number has two or more factors.
Which of the following numbers has the most factor pairs?
A) 13
B) 29
C) 48
D) 50
C (48) has 5 factor pairs: (1×48),(2×24),(3×16),(4×12),(6×8).
Daysi and Dylan are saving money to buy a computer game that costs $84. Each week, they deposit $12 into their savings jar. Use an input-output relationship to determine during which week they will meet their goal of having at least $84.
Week (X) Total Saved (Y)
1 $12
2 $24
3 $36
Week 7
Analyze the chart below showing Gwinnett County Students’ Favorite Ice Cream Flavors:
Ice Cream Flavor Number of Students
Vanilla 30,000
Strawberry 15,000
Chocolate 45,000
Mint Chocolate Chip 40,000
Cookie Dough 20,000
Which question below can be answered using the data in the chart?
A) How many 4th graders chose Strawberry as their favorite flavor?
B) How many more students chose Chocolate than Vanilla?
C) How many students were absent on the day of the survey?
D) Which ice cream brand is the most popular in the school district?
B is correct because the chart gives the total student counts for both Chocolate (45,000) and Vanilla (30,000), so you can subtract them ($45,000 - 30,000 = 15,000$).
Consider the number 36. Is 36 prime or composite? How do you know?
Use what you know about factors and multiples to describe the number 36 as prime or composite.
Factors:
Multiples:
Prime or Composite:
Because 36 has nine factors (1, 2, 3, 4, 6, 9, 12, 18, and 36),and it is a composite number.
I am a 2-digit number less than 50. I am a common multiple of 4 and 6, and I have exactly 8 total factors. What number am I?
24
Is 86 a prime number or composite number? Explain your reasoning. List the factors of 86.
The factors of 86 are 1, 2, 43, and 86.
Find the 7th number in the pattern. Use the rule, Start at 12, and add 14 to find the 7th number.
12, 26, 40, 54, 68, 82, 96.
At a school book fair, students at Baldwin Elementary voted on their favorite book genres. The results were displayed in a number chart:
Mystery: 18
Adventure: 24
Fantasy: 12
Science Fiction: 16
If the librarian wants to make a pictograph to show this data where each book symbol 📖 represents 4 student votes, how many total book symbols will she need to draw for all four genres combined?
17 book symbols
Ms. Collins is packing cookies in plastic bags for her students on Friday. She wants each bag to be filled with exactly 4 cookies. Can Ms.Collins pack 64 cookies into the bags without any left over?
Part A: Use multiplication to show whether 64 is a multiple of 4.
Part B: Identify the two factors and the multiple in your equation, and state how many bags Ms.Collins can pack.
Part A: 4x16=64
Part B:
Factors: 4 (cookies per bag) and 16 (number of bags)
Multiple: 64 (total number of cookies)
Because 4 x 16 = 64, the total number of cookies (64) is a multiple of both 4 and 16. Since 64 is a multiple of 4, it can be evenly distributed without any cookies left over.