Divisibility Rules

Divisibility Rules Page 10 in textbook

What does it mean to be divisible? • Divisible  A whole number is divisible by another number if the remainder is 0 when the first number is divided by the second.

Rule • A whole number is divisible by 2: • if the ones digit is divisible by 2 • A whole number is EVEN if it is divisible by 2 (even #s: 0, 2, 4, 6, 8) • Examples: 2, 4, 6, 8, 10, 12, …

Are these numbers divisible by 2? • 2,320 • 3,135 • 78 • 11,292

Rule • A whole number is divisible by 3: • if the sum of the digits is divisible by 3 • Example: 3, 6, 9, 12, 15, 18, …

Are these numbers divisible by 3? • 80 8 + 0 = 8 Not divisible by 3! • 489 • 14,980 • 18,321

Rule • A whole number is divisible by 4: • If the number formed by the last two digits is divisible by 4. • Example: 4, 8, 12, …, 104, 112, …

Are these numbers divisible by 4? • 605 look at the last 2 digits: 05  NOT divisible by 4! • 80 • 9, 948 • 11, 292

Rule • A whole number is divisible by 5: • If the ones digit is a 0 or 5. • Example: 5, 10, 15, 20, 25, …

Are these numbers divisible by 5? • 45 look at the ones place: 5  YES it is divisible by 5! • 631 • 385 • 459

Rule • A whole number is divisible by 6: • If the number is divisible by BOTH 2 and 3. • Example: 6, 12, 18, 24, 30, …

Are these numbers divisible by 6? • 126 Check for 2: ends in 6 which is divisible by 2 Check for 3: 1 + 2 + 6 = 9 which is divisible by 3 So, YES it is divisible by 6 because it is divisible by both 2 AND 3! • 684 • 2, 835 • 1, 114

Rule • A whole number is divisible by 9: • If the sum of the digits is divisible by 9. • Example: 9, 18, 27, 36, 45, …

Are these numbers divisible by 9? • 60 6 + 0 = 6, So NO it is not divisible by 9 • 138 • 900 • 8, 505

Rule • A whole number is divisible by 10: • If the ones digit is 0. • Example: 10, 20, 30, 40, 50, …

Are these numbers divisible by 10? • 56 Look at the ones place  6, so NO! • 220 • 32,360 • 654

Divisibility Rules