42510011 0010 1010 1101 0001 0100 1011

Divisibility

SWBAT to use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10

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0011 0010 1010 1101 0001 0100 1011

What is divisibility?

• Divisibility – If a number goes into another number, without

a remainder– 351 is divisible by 9

• 9 goes into 351, 39 times with no remainder

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Divisibility Rules2

3

4

5

6

8

9

10

it is an even number (ends in 0, 2, 4, 6, 8)

the sum of its digits is divisible by 3

the last two digits form a number divisible by 4

it ends in a 0 or a 5

it is divisible by both 2 and 3

the last three digits form a number divisible by 8

the sum of its digits is divisible by 9

it ends in a 0

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Examples

• 333• 128• 7,535• 8,289• 99,483• 67,704

• 3,95_, by 10• 17,84_, by 3• 17,39_, by 5• 27,1_8, by 6• 37,6_3, by 9

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0011 0010 1010 1101 0001 0100 1011

Try These

• 128– 2, 4, 8

• 9410– 2, 5, 10

• 17,934– 2, 3, 6

• 270,228– 2, 3, 4, 6

• 243,05__; by 9– 4

• 13,__12; by 8 and by 3– 5

• 20,71___; by 4– 2 or 6

42510011 0010 1010 1101 0001 0100 1011

Prime and Composite Numbers

SWBAT identify prime and composite numbers

4251

0011 0010 1010 1101 0001 0100 1011

Definitions

• Prime number– A whole number greater than 1 that has exactly

two factors, itself and 1

• Composite number– A whole number greater than 1 that has more

than two factors

• The numbers 0 and 1 are neither prime nor composite.

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Examples

• Tell whether each number is prime, composite, or neither– 24– 35– 2– 9– 19– 21– 1– 10,011

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0011 0010 1010 1101 0001 0100 1011

Try These

• 0– neither

• 81– Composite, divisible by 9

• 41– Prime

• 51– Composite, divisible by 3

• 37,311 – Composite, divisible by 3

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Perfect Numbers

• A perfect number is the sum of all its factors, not including itself.– 6 has factors of 1, 2, 3, and 6– If you add 1 + 2 + 3 (all the factors, except for

itself), you get 6– A perfect number?