Prime Factorization

Question 1

What is a factor?

Answer 1

A number that divides another number evenly (no remainder)

Question 2

What is a product?

Answer 2

The result of multiplying two or more numbers

Question 3

What is a dividend?

Answer 3

The number being divided

Question 4

What is a divisor?

Answer 4

The number you divide by

Question 5

What does “prime number” mean?

Answer 5

A number with exactly two factors: 1 and itself

Question 6

What does “composite number” mean?

Answer 6

A number with more than two factors

Question 7

What is prime factorization?

Answer 7

Writing a number as a product of prime numbers

Question 8

What is the prime factorization of 12?

Answer 8

2 × 2 × 3 (or 2² × 3)

Question 9

What is the prime factorization of 18?

Answer 9

2 × 3 × 3 (or 2 × 3²)

Question 10

What is the prime factorization of 60?

Answer 10

2 × 2 × 3 × 5 (or 2² × 3 × 5)

Question 11

What is the prime factorization of 100?

Answer 11

2 × 2 × 5 × 5 (or 2² × 5²)

Question 12

What is the prime factorization of 72?

Answer 12

2 × 2 × 2 × 3 × 3 (or 2³ × 3²)

Question 13

True or False: 37 is prime.

Answer 13

True

Question 14

True or False: 51 is prime.

Answer 14

False (51 = 3 × 17)

Question 15

Find the prime factors of 90.

Answer 15

2 × 3 × 3 × 5 (or 2 × 3² × 5)

Question 16

Find the prime factors of 45.

Answer 16

3 × 3 × 5 (or 3² × 5)

Question 17

Find the prime factors of 84.

Answer 17

2 × 2 × 3 × 7 (or 2² × 3 × 7)

Question 18

Word Problem: A baker has 36 muffins and wants to package them equally with no leftovers. What is the greatest number of boxes he can use?

Answer 18

36 (use 1 muffin per box, factors of 36 allow multiple groupings)

Question 19

Word Problem: There are 24 students. They are divided into equal groups for a game with no one left out. What group sizes are possible?

Answer 19

1, 2, 3, 4, 6, 8, 12, 24 (factors of 24)

Question 20

Word Problem: You have 48 chocolates and want to arrange them into a perfect rectangle with no leftovers. What are possible arrangements?

Answer 20

Pairs of factors of 48: 1×48, 2×24, 3×16, 4×12, 6×8

Question 21

Word Problem: Two numbers have a product of 60. One number is 12. What is the other number?

Answer 21

5 (because 12 × 5 = 60)

Question 22

Word Problem: A number has prime factorization 2³ × 3. What number is it?

Answer 22

24

Question 23

Word Problem: The product of three primes is 105. What are the primes?

Answer 23

3 × 5 × 7

Question 24

Word Problem: A number is divisible by 2 and 5 but no other primes. What is the smallest number it can be?

Answer 24

10

Question 25

Which is a common factor of 18 and 24?

Answer 25

6

Question 26

What is the greatest common factor (GCF) of 36 and 48?

Answer 26

12

Question 27

What is the least common multiple (LCM) of 6 and 8?

Answer 27

24

Question 28

Word Problem: You want to arrange 20 chairs in rows with the same number in each row. What are all possible row sizes?

Answer 28

1, 2, 4, 5, 10, 20

Question 29

Word Problem: A number has 2, 3, and 11 as prime factors. What is the number?

Answer 29

66

Question 30

What is the difference between a factor and a multiple?

Answer 30

A factor divides the number; a multiple is what you get when you multiply the number by something

Question 31

Explain why 1 is neither prime nor composite.

Answer 31

It only has one factor (1), not two