Factors and Divisibility

Divisibility Rules

by HSP EDU

​Why it is helpful to know divisibility rules:

• It helps to find the prime factorization of numbers

• ​It helps with finding GCF

• ​It helps with reducing fractions

Multiple Choice

Which number is divisible by 2, 3, and 6?

• 60

• 33

• 46

• 21

Multiple Choice

A number is divisible by 2 if:

• the sum of its digits is divisible by 2.

• it ends in a 0.

• it is an even number (ends in a 0,2,4,6,8)

• it ends in a 0 or 5.

Multiple Choice

A number is divisible by 3 if:

• the sum of its digits is divisible by 3.

• it ends in a 0.

• it is an even number (ends in a 0,2,4,6,8)

• it ends in a 0 or 5.

Multiple Choice

A number is divisible by 5 if:

• the sum of its digits is divisible by 3.

• it ends in a 0.

• it is an even number (ends in a 0,2,4,6,8)

• it ends in a 0 or 5.

Multiple Choice

A number is divisible by 10 if:

• the sum of its digits is divisible by 3.

• it ends in a 0.

• it is an even number (ends in a 0,2,4,6,8)

• it ends in a 0 or 5.

Multiple Choice

Factors are

• even numbers

• odd numbers

• numbers that we multiply to get a product.

• an answer when you divide

Multiple Select

Choose all the factors of 18.

• 1, 18

• 3, 5

• 3, 6

• 2, 9

Multiple Select

Choose all that represent factors of 15

• 3,5

• 2,8

• 1, 15

Multiple Choice

Is 565 divisible by 2?

• Yes

• No

Multiple Choice

Is 324 divisible by 3?

• Yes

• No

Multiple Choice

2520 is divisible by 6 because:

• It is divisible by 2 (even) and 5 (ends in a 0 or 5)

• The sum of the digits is 12, a multiple of 6

• It's divisible by 2 (even) and 3 (sum of digits is a multiple of 3)

• The sum of the digits is even

Multiple Choice

Which of these is divisible by 9?

• 9629
• 9199
• 9963
• 4919

What are Prime numbers?

• Whole numbers greater than 1 that only have two factors, 1 and itself

• Prime numbers are only divisible by 1 or itself

• Example: 2 is prime because the only two factors are 1 and 2, (1 x 2 = 2): 11 is prime number because the only two factors are 1 and 11 (1 x11=11).

• Can you list the first 10 prime numbers?

Composite Numbers

• Whole numbers greater than 1 that are not prime numbers.

• Composite numbers have more than 2 factors.

• 4 is a composite number because it's factors are 1, 2, and 4.

Multiple Choice

Which list has only prime numbers?

• 2, 3, 4, 5
• 1, 5, 7, 9
• 2, 3, 5, 7
• 2, 4, 6, 8

Multiple Choice

What is the Prime Factorization of 128?

• 
  

  $$7^2$$

• $$2^7$$
  

• $$32\times4$$

• $$16\times8$$

Multiple Choice

What is the prime factorization of 48?

• $$2\times24$$

• $$3\times16$$

• $$4^2\times3$$

• $$2^4\times3$$

Multiple Choice

Find the prime factorization of 81

• 2² • 7

• 2³ • 5 • 7

• 4³

• 3⁴

Greatest Common Factor (GCF)

• The greatest shared factor between two numbers.

• You can use prime factorization as a strategy to find the GCF of 2 numbers.

• The GCF of two numbers will always be the smaller of the two numbers or less

Multiple Choice

Find the greatest common factor of 20 and 30

• 2
• 5
• 10
• 15

Multiple Choice

What is the Greatest Common Factor of 48 and 32 and 16

• 1

• 2

• 16

• 48