Divisibility Rules and Finding Factors Pre-Algebra Section 4-1

Divisibility Rules: What are they? Rules to help you determine if numbers are divisible by other numbers. Divisible – if a number can be divided by another number with no remainder, decimal, or fraction. We will learn rules for 2, 3, 4, 5, 6, 8, 9, and 10.

Divisibility Rule for 2 A number is divisible by 2 if… The number is even. Even numbers end in 2, 4, 6, 8, or 0. Examples 412 230 516

Divisibility Rule for 10 A number is divisible by 10 if… The number ends in a zero. Examples 4,000 210 50

Divisibility Rule for 5 A number is divisible by 5 if… The number ends in a 5 or 0. Examples 4,000 215 355

Divisibility Rule for 3 A number is divisible by 3 if… The sum of the digits of the number is divisible by 3. Examples 354 3 + 5 + 4 = 12 12 / 3 = 4 9,363,129 9 + 3 + 6 + 3 + 1 + 2 + 9 = 33 33/3 = 11

Divisibility Rule for 9 A number is divisible by 9 if… The sum of the digits of the number is divisible by 9. Examples 495 4 + 9 + 5 = 18 18 / 9 = 2 999,918 9 + 9 + 9 + 9 + 1 + 8 = 45 45 / 9 = 5

Divisibility Rule for 6 A number is divisible by 6 if… The number is divisible by both 3 and 2. Examples 930 6000 216

Divisibility Rule for 4 A number is divisible by 4 if… The last 2 digits of the number is divisible by 4. Examples 9,264 1,209,124 216

Divisibility Rule for 8 A number is divisible by 8 if… The last 3 digits of the number are divisible by 8. Examples 9,808 8,942,216 848

Divisibility Rules A number is divisible by: 2 if the number is even. 3 if the sum of the digits is divisible by 3. 4 if the last 2 digits of the number are ÷ by 4. 5 if the number ends in a 5 or 0. 6 if the number is divisible by 2 and 3. 8 if the last 3 digits of the number are ÷ by 8. 9 if the sum of the digits is divisible by 9. 10 if the number ends in a 0.

What number(s) is the number below divisible by? 75 3 and 5

What number(s) is the number below divisible by? 111 3

What number(s) is the number below divisible by? 131 None

What number(s) is the number below divisible by? 2,848 2, 4, and 8

What number(s) is the number below divisible by? 9,540 2, 3, 4, 5, 6, 9, and 10

What number(s) is the number below divisible by? 144 2, 3, 4, 6, 8, and 9

Factors What is a factor of a number? An integer that divides into another integer with a remainder of zero. How can you find a number’s factors? Make an organized list of the all of the problems (multiplication facts) that make that number. 18

Listing Factors (Example 1) List the positive factors for 54 1 x 54 2 x 27 3 x 18 6 x 9 1, 2, 3, 6, 9, 18, 27, and 54 19

Listing Factors (Example 2) List the positive factors for 28 1 x 28 2 x 14 4 x 7 1, 2, 4, 7, 14, and 28 20

Listing Factors (Example 3) List the positive factors for 64 1 x 64 2 x 32 4 x 16 8 x 8 1, 2, 4, 8, 16, 32, and 64 21