Frank and Denny are best friends. They have many common interests. They both enjoy hockey, playing video games, and reading mysteries.
In this activity you will list the common factors of two or more numbers.
A common factor of two or more numbers is a factor of each of the numbers.
You can use T-tables to find the common factors of two or more numbers.
List the common factors of 24 and 30.
Step 1: List all the factors of 24 and all the factors of 30.
Step 2: Circle the common factors of 24 and 30. That is, circle the numbers that are in both T-tables.
The common factors of 24 and 30 are 1, 2, 3, and 6.
1. Use T-tables to list the common factors for each pair of numbers.
a. 24 and 36 b. 12 and 18 c. 30 and 75
Often it is useful to find the greatest common factor (GCF) of two or more numbers.
The greatest common factor of two or more numbers is the greatest number in the list of common factors of the numbers.
A grocer wants to make up gift packages that contain two kinds of candy. Each package must have the same number of candies. One type of candy comes in boxes that contain 18 pieces and the other comes in bags that contain 24 pieces. What is the greatest number of gift packages that the grocer can make from a box of one type of candy and a bag of the other type?
Step 1: List all the factors of 18 and all the factors of 24.
Step 2: Circle the common factors of 18 and 24.
The common factors of 18 and 24 are 1, 2, 3, and 6.
Step 3: Choose the greatest number in the list of common factors.
The greatest common factor of 18 and 24 is 6.
So, the greatest number of gift packages that the grocer can make from one box and one bag is 6.
2. Find the greatest common factor for each of these pairs of numbers.
a. 6 and 12 b. 30 and 45 c. 42 and 56
3. What is the greatest common factor of each of these sets of numbers?
a. 54, 81, and 63 b. 8, 16, and 20 c. 24, 42, and 48
4. Jeanine, Julie, and Joyce bought some jawbreakers at the same candy store. Jeanine bought 28¢ worth, Julie bought 72¢ worth, and Joyce bought 96¢ worth. What is the most that each jawbreaker could have cost?
Use the Internet to discover the nationality of each of these ancient mathematicians: Thales (624–546 B.C.), Pythagoras (585–507 B.C.), Archimedes (287–212 B.C.), and Apollonius (262–190 B.C.).
Hint: The MacTutor History of Mathematics archive on the World Wide Web has an alphabetical index of mathematicians.
5. The planet Venus circles the Sun in a highly elliptical or egg-shaped orbit, ranging between 109 000 000 km from the Sun and about 107 000 000 km from the Sun.
About how much farther from the Sun is Venus when it is at its farthest point, as compared to when it is at its closest point?
