3.1 Prime and Composite Numbers
Divisibility rules, prime factorization of a composite number, and greatest common divisor and least common multiple applied to word problems.
23 exercises
3.1 Exercise 1
Determine if 36 is divisible by 4.
3.1 Exercise 3
Using divisibility rules, determine if 245 is divisible by 5.
3.1 Exercise 5
Using divisibility rules, determine if 25,983 is divisible by 9.
3.1 Exercise 7
Can 298 coins be stacked into 6 stacks with an equal number of coins in each stack?
3.1 Exercise 9
Using divisibility rules, determine if 4,259 is divisible by 10.
3.1 Exercise 11
Using divisibility rules, determine if 936,276 is divisible by 4.
3.1 Exercise 13
Determine if 2,117 is prime or composite.
3.1 Exercise 15
Determine if 423 is prime or composite.
3.1 Exercise 17
Determine if 1,034 is prime or composite
3.1 Exercise 19
Determine if 2,917 is prime or composite.
3.1 Exercise 21
Find the prime factorization of 140.
3.1 Exercise 27
How many different prime factors does 10,241 have?
3.1 Exercise 29
Find the greatest common divisor of 1,400 and 250 by listing all divisors of each number.
3.1 Exercise 31
Find the greatest common divisor of 1,400 and 250 by using their prime factorizations.
3.1 Exercise 33
Find the greatest common divisor of 600 and 784 by using their prime factorizations.
3.1 Exercise 35
Suppose you have a rectangular room that is 570 cm wide and 450 cm long. You wish to cover the floor of the room with square tiles. What’s the largest size square tile that can be used to cover this floor?
3.1 Exercise 37
Suppose you want to organize books onto shelves, and you want the shelves to hold the same number of books. Each shelf will only contain one genre of book. You have 24 sci-fi, 42 fantasy, and 30 horror books. How many books can go on each shelf?
3.1 Exercise 39
Find the LCM of 24 and 90 by listing multiples and choosing the smallest common multiple.
3.1 Exercise 41
Use the prime factorizations of 24 and 90 to identify their LCM.
3.1 Exercise 43
Use the prime factorizations of 36, 66, and 250 to identify the LCM.
3.1 Exercise 45
Find the LCM of 20, 36, and 45 using lists and prime factorization.
3.1 Exercise 47
Two students, João, and Amelia, meet one day at an assisted living facility where they volunteer. João volunteers every 6 days. Amelia volunteers every 10 days. How many days will it be until they are both volunteering on the same day again?
3.1 Exercise 49
A team-building exercise has teams build a house of cards as high as possible. However, the cards for different teams are of different sizes. Team 1 uses 10 cm × 10 cm cards, while Team 2 uses 8 cm × 8 cm cards. What is the minimum height when the two teams will be tied? Ignore the width of the cards.
Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.