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Divisibility rules

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“Divisible by” From Lessons 1-4, we learned that number is “divisible by” another number when there is no remainder. Example: 21 is divisible by 7 (21 ÷ 7 = 3) 48 is divisible by 4 (48 ÷ 4 = 12) 24 is not divisible by 5 (24 ÷ 5 = 4 r 4) 33 is not divisible by 2 (33 ÷ 2 = 16 r 1)

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Calculator Test One way to determine if a number is divisible by another is to use a calculator. If the division gives results in a decimal, it is not divisible by that number Example: Look at these two calculations; which is not divisible by 2? 341 ÷ 2 = ÷ 2 = 124

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**Calculator Test continued**

341 ÷ 2 = 170.5 341 is not divisible by 2 (The quotient has a decimal, 170.5) 248 ÷ 2 = 124 248 is divisible by 2 (The quotient has no decimal, 124)

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Divisibility Rules How can you know that a number is divisible by 2 without actually doing the division?

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Divisibility Rules How can you know that a number is divisible by 2 without actually doing the division? Numbers that end in 0, 2, 4, 6, or 8 are divisible by 2. Examples: 20, 14, 436, 208

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**Can you tell whether a number is divisible by 10 without dividing?**

Divisibility Rules Can you tell whether a number is divisible by 10 without dividing?

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Divisibility Rules Can you tell whether a number is divisible by 10 without dividing? Yes, numbers that end in zero are divisible by 10. examples: 20, 100, 250, 1030

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**Can you tell whether a number is divisible by 3 without dividing?**

Divisibility Rules Can you tell whether a number is divisible by 3 without dividing?

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Divisibility Rules Can you tell whether a number is divisible by 3 without dividing? Yes, but first you must know about DIGITAL SUMS.

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Digital Sums What is a DIGITAL SUM? Examples: The digital sum of 348 is 15. (3+4+8=15) The digital sum of 1,045 is 10. ( =10) The digital sum of 111 is 3. (1+1+1=3) The digital sum of 712,004 is 14 ( =14)

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**Yes, if the digital sum is divisible by 3, so is the number.**

Divisibility Rules Can you tell whether a number is divisible by 3 without dividing? Yes, if the digital sum is divisible by 3, so is the number. 201 is divisible by 3: (2+0+1=3 and 3÷3=1 )

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**Divisible by 3 EXAMPLES: 123 is divisible by 3:**

The Digital Sum of 123 is 6 (1+2+3=6) 6 ÷ 3 = 2 452 is not divisible by 3 The Digital Sum of 452 is 11 (4+5+2=11) 11 ÷ 3 = 3r2

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Divisibility RAP

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**DIGITAL SUMS also works for numbers divisible by 9.**

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Digital Sums and 9s Examples 603 is divisible by 9: The Digital Sum of 603 is 9 (6+0+3=9) 9 ÷ 9 = is divisible by 9 The Digital Sum of 459 is 18 (4+5+9=18) 18 ÷ 9 = 2

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**Is 936 divisible by both 3 and 9?**

Digit Sums Is 936 divisible by both 3 and 9?

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Digit Sums Is 936 divisible by both 3 and 9? Digital Sum of 936 is ÷ 3 = 6 18 ÷ 9 = = 2 Yes, 936 is divisible by both 3 and 9.

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**Is 444 divisible by both 3 and 9?**

Digit Sums Is 444 divisible by both 3 and 9?

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Digit Sums Is 444 divisible by both 3 and 9? Digital Sum of 444 is ÷ 3 = 4 12 ÷ 9 = = 1r3 No, 444 is divisible by 3 (but not 9).

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Video segment #2 Digital Sums song One more 3 and 9 explanation:

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Divisibility Test for 5 How can you tell if these numbers are divisible by 5? 20; 35; 70; 100; 25; 109,005

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Divisibility Test for 5 How can you tell if these numbers are divisible by 5? 20; 35; 70; 100; 25; 109,005 The last digit is always a 0 or 5.

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**Divisibility Test for 6 702 is divisible by 6. Why?**

It is an EVEN number and the DIGIT SUM is divisible by 3. 702 is EVEN 7+0+2=9 (9÷3=3)

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**Divisibility Test for 6 501 is NOT divisible by 6. Why?**

BOTH of these MUST BE TRUE: EVEN Digit Sum is divisible by 3 501 is ODD 5+0+1=6 (6÷3=2)

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Divisibility Test for 4 Ignore all digits except for the last two: 432, ÷ 4 = ÷4=6

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