Divisibility rules

“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)

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 = 170.5 248 ÷ 2 = 124

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)

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

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

Divisibility Rules 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?

Yes, numbers that end in zero are divisible by 10.

examples: 20, 100, 250, 1030

Divisibility Rules 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?

Yes, but first you must know about

DIGITAL SUMS.

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. (1+0+4+5=10) The digital sum of 111 is 3. (1+1+1=3) The digital sum of 712,004 is 14 (7+1+2+0+0+4=14)

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 )

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

Divisibility RAP  http://www.youtube.com/watch?v=GqulDDVocLo& NR=1

DIGITAL SUMS

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 = 1 459 is divisible by 9 The Digital Sum of 459 is 18 (4+5+9=18) 18 ÷ 9 = 2

Digit Sums Is 936 divisible by both 3 and 9?

Digit Sums Is 936 divisible by both 3 and 9?

Digital Sum of 936 is 18.

18 ÷ 3 = 6 18 ÷ 9 = = 2 Yes, 936 is divisible by both 3 and 9.

Digit Sums Is 444 divisible by both 3 and 9?

Digit Sums Is 444 divisible by both 3 and 9?

Digital Sum of 444 is 12.

12 ÷ 3 = 4 12 ÷ 9 = = 1r3 No, 444 is divisible by 3 (but not 9).

Video segment #2 Digital Sums song http://www.youtube.com/watch?v=1ffvCtNZN9Q One more 3 and 9 explanation: http://www.youtube.com/watch?v=_-IbZ5Ih_nU

Divisibility Test for 5 How can you tell if these numbers are divisible by 5?

20; 35; 70; 100; 25; 109,005

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.

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)

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)

Divisibility Test for 4 Ignore all digits except for the last two: 432,712 432,7 12 12 ÷ 4 = 3 ---------------------------------------------------------------- 1324 13 24 24÷4=6