Multiples
A multiple is a number that divides another number without leaving a remainder.
a) True
b) False
b) False. That was the definition of a factor! A multiple is the result of a number multiplied by an integer.
What is the definition of a factor?
A number that divides another number without leaving a remainder.
What is Prime Factorization?
Bonus: What is the only even prime number?
The process of writing a number as the product of primes.
2.
Explain why every multiple of 4 is even.
4 = 2(2n). For any integer k, 4 x k = 2(2n) x k.
Since 4 is even, any multiple of 4 will also be even.
A common factor is a divisor of 2 or more different numbers.
a) True
b) False
a) True
What is the prime factorization of 72 in simplified notation (using powers)?
23 x 32
Which of the following statements is TRUE?
a) 48 is a common multiple of 6 and 9
b) 3 is a common multiple of 12
c) 36 is a common multiple of 4 and 3
c) 36 is a common multiple of 4 and 3
What the 3 common factors of 96, 24, and 32 (not including 1).
2,4,8
The prime factorization of 360 is 2 x 2 x 2 x 3 x 3 x 5. How could we simplify this by using powers?
The simplified prime factorization is 23 x 32 x 5.
Which number could be the difference between two multiples of 8?
A. 91
B. 75
C. 24
D. 33
C. 24 because it is the only option that is a multiple of 8.
Find the GREATEST common factor of 63, 77, and 91.
7.
Solve this riddle: I am a number whose prime factors are all of the prime numbers between 6 and 15. No factor is repeated. What number am I?
You are 1001 because 7 x 11 x 13
Beginning at 8:30 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?
A. Every 15 minutes
B. Every 30 minutes
C. Every 45 minutes
D. Every 60 minutes
D. Every 60 minutes
Nadia baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?
6. First find all the factors of 30 and 48. What are the common factors between 30 and 48? Now which of these is the HIGHEST number?
What is the largest prime number in the prime factorization of 176?
11. Because 176 = 11 x 24