Prime Numbers

Composite Numbers

Factors

Prime Factorization (Factor Trees)

Multiples

Least Common Multiple

Greatest Common Factor

Divisibility Rules

Number It is divisible if… Examples Examples that to support do not work.

2 A number ends in 0, 2, 4, 6, 8

10, 12, 14 15, 17, 7936, 98

3 The sum of the digits is divisible by 3

3, 6, 12, 135 142, 17, 23

4 If the last two digits are divisible by 4 or the number ends in 00.

44, 100, 124 41, 77, 38 120, 112 114, 14

5 If the number ends in 5 or 0.

10, 25, 55, 135 41, 77, 88

6 If the number is divisible by 2 and 3.

6, 12, 24, 19, 44, 50

9 If the sum of the digits is divisible by 9.

9, 18, 189, 981 38, 980, 98

10 If the number ends in 0. 10, 20, 30, 1090 125, 38, 88

A PRIME number is a number that has only two factors: 1 and itself.

Example:

2: only 1 and 2 will go into 2

3: only 1 and 3 will go into 3

5: only 1 and 5 will go into 5

Other prime numbers are :

7, 11, 13, 17, 19, 23, and many more!

Greatest common Factor (GCF)

To find the GCF do the following:

Step 1: List all the factors for each number

Step 2: Find the largest factor these two numbers have in common

Example:

Find the GCF for 60 and 72

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The largest number 60 and 72 have in common is 12, therefore the GCF = 12

To find the least common multiple do the following:

Step 1: List the multiples for each number

Step 2: Find the smallest number they have in common other than zero.

Example:

Find the LCM for 7 and 5

7: 0, 7, 14, 21, 28, 35, 42, …

5: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, …

Least Common Multiple

List the factors each number. Then check your answer by clicking the “CHECK” button.

1. List the factors of 8:

2. List the factors of 10:

3. List the factors of 4:

4. List the factors of 20:

5. List the factors of 16:

6. List the factors of 25:

7. List the factors of 100:

8. List the factors of 3:

REVIEW

CHECK

List the factors each number. Then check your answer by clicking the “CHECK” button.

1. List the factors of 8: 1, 2, 4, 8

2. List the factors of 10: 1, 2, 5, 10

3. List the factors of 4: 1, 2, 4

4. List the factors of 20: 1, 2, 4, 5, 10, 20

5. List the factors of 16: 1, 2, 4, 8, 16

6. List the factors of 25: 1, 5, 25

7. List the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

8. List the factors of 3: 1, 3

REVIEW

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Composite numbers are numbers that have more than two factors.

Example:

4: 1, 2 and 4 go into 4

6: 1, 2 , 3 and 6 go into 6

8: 1, 2, 4, and 8 go into 8.

Factors are numbers that go into another number. To find the factors of a number, find the pairs.

Example:

Factors of 20

1 x 20

2 x 10

4 x 5

20: 1, 2, 4, 5, 10, 20Then write them in order from least to greatest! Then write them in order from least to greatest!

Factors of 50:

1 x 50

2 x 25

5 x 5

50: 1, 2, 5, 25, 50

Remember: A factor will never be larger than the number itself.

QUIZ

Factor Trees are used to find the PRIME FACTORIZATION of a number.

70

35 2

5 7Prime Factorization of

70 is: 2 x 5 x 7

Circle the number if it is prime

QUIZ

Multiples are all the numbers a number will go into. Multiples are infinite!

Examples:

Multiples of :

5: 0, 5, 10, 15, 20, …

3: 0, 3, 6, 9, 12, 15, 18, …

20: 0, 20, 40, 60, …

0 is the first multiple of every number.

Multiples are infinite, so you must end each

line with … to show infinity.

QUIZ

List the prime factorization for each number. Then check your answer by clicking the “CHECK” button.

1. 72

2. 50

3. 100

4. 90

5. 20

6. 15REVIEW

CHECK

1. 72: 2 x 3

2. 50: 5 x 2

3. 100: 5 x 2

4. 90: 3 x 5 x 2

5. 20: 2 x 5

6. 15: 3 x 5

REVIEW

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2

2

2 2

2

3

2

List the multiples for each number. Then check your answer by clicking the “CHECK” button.

1. List the multiples of 8:

2. List the multiples of 10:

3. List the multiples of 4:

4. List the multiples of 20:

5. List the multiples of 16:

6. List the multiples of 25:

7. List the multiples of 100:

8. List the multiples of 3:

CHECK

REVIEW

1. List the multiples of 8: 0, 8, 16, 24, 32, …

2. List the multiples of 10: 0, 10, 20, 30, 40,…

3. List the multiples of 4: 0, 4, 8, 12, 16, …

4. List the multiples of 20: 0, 20, 40, 60, 80, …

5. List the multiples of 16: 0, 16, 32, 48, 64, …

6. List the multiples of 25: 0, 25, 50, 75, 100, …

7. List the multiples of 100: 0, 100, 200, 300, 400, …

8. List the multiples of 3: 0, 3, 6, 9, 12, …

REVIEWBACK TO THE QUIZ