Download 6.1-6.2 Divisibility, Prime and Composite

Divisibility
0011 0010 1010 1101 0001 0100 1011
1
2
4
SWBAT to use divisibility rules for
2, 3, 4, 5, 6, 8, 9, and 10
What is divisibility?
0011 0010 1010 1101 0001 0100 1011
• Divisibility
– If a number goes into another number, without
a remainder
– 351 is divisible by 9
1
2
4
• 9 goes into 351, 39 times with no remainder
Divisibility Rules
2
it is an even number (ends in 0, 2, 4, 6, 8)
0011 0010 1010 1101 0001 0100 1011
3
the sum of its digits is divisible by 3
4
the last two digits form a number divisible by 4
5
it ends in a 0 or a 5
6
it is divisible by both 2 and 3
8
the last three digits form a number divisible by 8
9
the sum of its digits is divisible by 9
10
it ends in a 0
1
2
4
Examples
0011 0010 1010 1101 0001 0100 1011
•
•
•
•
•
•
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
1
2
4
Try These
0011 0010 1010 1101 0001 0100 1011
• 128
– 2, 4, 8
• 9410
– 2, 5, 10
• 17,934
– 2, 3, 6
• 270,228
– 2, 3, 4, 6
• 243,05__; by 9
– 4
2
• 13,__12; by 8 and by 3
– 5
1
• 20,71___; by 4
– 2 or 6
4
Prime and Composite Numbers
0011 0010 1010 1101 0001 0100 1011
1
2
4
SWBAT identify prime and
composite numbers
Definitions
0011 0010 1010 1101 0001 0100 1011
• Prime number
– A whole number greater than 1 that has exactly
two factors, itself and 1
• Composite number
1
2
4
– A whole number greater than 1 that has more
than two factors
• The numbers 0 and 1 are neither prime nor
composite.
Examples
0011 0010 1010 1101 0001 0100 1011
• Tell whether each number is prime, composite, or
neither
–
–
–
–
–
–
–
–
24
35
2
9
19
21
1
10,011
1
2
4
Try These
0011 0010 1010 1101 0001 0100 1011
• 0
– neither
• 81
– Composite, divisible by 9
• 41
– Prime
• 51
– Composite, divisible by 3
• 37,311
– Composite, divisible by 3
1
2
4
Perfect Numbers
0011 0010 1010 1101 0001 0100 1011
• A perfect number is the sum of all its
factors, not including itself.
1
2
– 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?
4