1. Tyler has 45 baseball cards and 54 basketball cards. He organized them into equal rows for a display. He did not want to mix the basketball and baseball cards in a row. What was the greatest number of cards in each row?
a. Write each number as the product of any two of its factors.
b. Continue to write each factor as the product of two factors until only prime factors remain.
c.Write the prime factorization for each original number. Highlight the common prime factors.
d. Find the product of the common prime factors.
e. Whats the Greatest Common Factor [GCF]?
DOGHOUSING! [2-4.]
a.18 and 24.
b.64 and 80.
c.84 and 56.
5. Two sixth grade classes went to the local theater to watch a movie. They reserved seats ahead of time so each class could sit together in equal rows. One class had 28 students and the other had 21 students. What is the greatest number of students that could sit in each row?
6. Camilla separated prizes for games at the carnival. She had 72 choco bars and 90 peanut blitzes. She put the most candy bars possible in each bag without mixing the two types. Each bag needed a equal amount of candy. How many candy bars did she put in each bag?
1.
a. Write each number as the product of any two of its factors.
b. Continue to write each factor as the product of two factors until only prime factors remain.
c.Write the prime factorization for each original number. Highlight the common prime factors.
d. Find the product of the common prime factors.
e. Whats the Greatest Common Factor [GCF]?
To find the greatest number of cards or students that can be placed in each row or bag, we need to find the greatest common factor (GCF) of the given numbers.
1. Tyler's cards:
- Baseball cards: 45 (prime factorization: 3 * 3 * 5)
- Basketball cards: 54 (prime factorization: 2 * 3 * 3 * 3)
We need to find the common factors between these two numbers. The common prime factors are 3 and 3 (highlighted).
So, the product of the common prime factors (GCF) is 3 * 3 = 9.
Therefore, the greatest number of cards in each row is 9.
5. Two sixth-grade classes:
- First class: 28 students (prime factorization: 2 * 2 * 7)
- Second class: 21 students (prime factorization: 3 * 7)
The common prime factors are 7 (highlighted).
Therefore, the greatest number of students that can sit in each row is 7.
6. Camilla's candy bars:
- Choco bars: 72 (prime factorization: 2 * 2 * 2 * 3 * 3)
- Peanut Blitzes: 90 (prime factorization: 2 * 3 * 3 * 5)
The common prime factors are 2, 3, and 3 (highlighted).
Therefore, the greatest number of candy bars she can put in each bag is 2 * 3 * 3 = 18.