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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?
1. 2,320
2. 3,135
3. 78
4. 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?
1) 808 + 0 = 8 Not divisible by 3!
2) 489
3) 14,980
4) 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?
1) 605look at the last 2 digits: 05 NOT divisible by 4!
2) 80
3) 9, 948
4) 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?
1) 45look at the ones place: 5 YES it is divisible by 5!
2) 631
3) 385
4) 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?
1) 126Check for 2: ends in 6 which is
divisible by 2Check for 3: 1 + 2 + 6 = 9 which is divisible
by 3So, YES it is divisible by 6 because it is
divisible by both 2 AND 3!2) 684
3) 2, 835
4) 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?
1) 606 + 0 = 6, So NO it is not divisible
by 92) 138
3) 900
4) 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?
1) 56Look at the ones place 6, so NO!
2) 220
3) 32,360
4) 654
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