NUMBER THEORY & FRACTIONS

PRIME & COMPOSITE

100

Is 37 prime or composite?

Prime

200

Give all composite numbers between 20 and 25.

21, 22, 24

300

What is the prime factorization of 28?

2² x 7

400

True or False: 51 is composite.

true (51 = 3 x 17)

500

A number has exactly three positive factors. Give one possible number and explain why.

Any perfect square of a prime → 4 (1,2,4), 9 (1,3,9), 25 (1,5,25).
Because only perfect squares of primes have exactly 3 factors.

GCF

100

List the common factors of 8 and 12.

1, 2, 4

200

What is the GCF of 18 and 24?

6

300

What is the GCF of 36 and 54?

18

400

What is the greatest common factor of 15, 20, and 35?

5

500

A number has a GCF of 14 with 42. What could the number be? Give two possible answers.

Any number whose factors include 2 × 7 but no higher shared factors.
Examples: 14, 28, 56, 70, 84…
(Minimum: 14; Maximum: infinite options)

FRACTION ESTIMATION & EQUIVALENTS

100

Is 3/20 closer to 0, ½, or 1?

0

200

Write an equivalent fraction to 2/3.

4/6, 6/9, 8/12 …

300

Is 9/16 closer to 0, ½, or 1?

Closer to ½

400

Which is larger: 5/12 or 3/7?

5/12 ≈ 0.416
3/7 ≈ 0.428
→ 3/7 is larger

500

A fraction is very close to 1. If its denominator is 200, give a numerator that makes it closer to 1 than ¾.

Must be greater than 150.
Examples: 160/200, 175/200, 190/200, 199/200…

LCM & COMMON MULTIPLES

100

What is the LCM of 4 and 6?

12

200

List the first 3 common multiples of 3 and 5.

15, 30, 45

300

What is the LCM of 8 and 12?

24

400

What is the smallest number that is a multiple of both 9 and 15?

45

500

The LCM of two numbers is 84. One of the numbers is 12.
Give two possible values for the second number.

Numbers whose LCM with 12 = 84 → 7, 14, 21, 28, 42, 84

DIVISION & INTERPRETING REMAINDERS

100

9 ÷ 2 = ? (Write in mixed number form)

4½

200

If 23 kids get into cars that hold 4 each, how many cars are needed?

Round up → 6 cars

300

15 ÷ 7 = ?

2 1/7

400

Tanner buys notebooks. Each costs $3. If he has $20, how many can he buy?

6 notebooks (round down)

500

A zookeeper needs to divide 247 grams of food equally into 12 habitats.

• Write the exact mixed number.

• Determine whether she should round up, round down, or keep the fraction.

247 ÷ 12 = 20 7/12
Interpretation: Keep the fraction, because food can be measured in partial grams.