Download Divisibility Rules

Divisibility Rules
A number is divisible by 2
• If the last digit is even
• Divisible: 3,978
• Not Divisible: 4,975
A number is divisible by 3
• If the sum of the digits is divisible by 3
• Divisible: 315 (3 + 1 + 5 = 9; 9 is divisible
by 3)
• Not Divisible: 139 (1 + 3 + 9 = 13; 13 is not
divisible by 3)
A number is divisible by 4
• If the last two digits form a number divisible
by 4.
• Divisible: 8,512 (12 is divisible by 4)
• Not Divisible: 7,518 (18 is not divisible by 4)
A number is divisible by 5
• If the last digit is 0 or 5
• Divisible: 14,975
• Not Divisible: 10, 978
A number is divisible by 6
• If the number is divisible by both 2 and 3
• Divisible: 48
– the last digit is even – divisible by 2
– 4 + 8 = 12; 12 is divisible by 3
• Not Divisible: 20
– the last digit is even – divisible by 2
– 2 + 0 = 2; 2 is not divisible by 3
A number is divisible by 9
• If the sum of the digits is divisible by 9
• Divisible: 711 (7 + 1 + 1 = 9; 9 is divisible
by 9
• Not Divisible: 93 (9 + 3 = 12; 12 is not
divisible by 9)
A number is divisible by 10
• If the last digit is 0
• Divisible: 15, 990
• Not Divisible: 10,536
•EXAMPLE
Tell whether 741 is divisible by 2, 3,
4, 5, 6, 9, and 10
2: The last digit is odd – NO
3: 7 + 4 + 1 = 12; 12 is divisible by 3 – YES
4: The last two digits form the number 41. 41 isn’t
divisible by 4 – NO
5: The last digit is 1 – NO
6: Divisible by 3, but not by 2 – NO
9: 7 + 4 + 1 = 12; 12 isn’t divisible by 9 – NO
10: The last digit is 1 – NO
741 is divisible by 3
Prime Numbers
Any number divisible by 1 and itself.
Ex: 2, 3, 5, 7, 11, …
Composite Numbers
• A number greater than 1 that has 2 (or
more) whole number factors
EX: 6 (2, 3)
20 (2, 4, 5, 10)
What number is neither prime
nor composite?
1
PRACTICE
Tell whether each number is
divisible by 2, 3, 4, 5, 6, 9, or 10
810
2: The last digit is even – YES
3: 8 + 1 + 0 = 9; 9 is divisible by 3 - YES
4: The last two digits form the number 10. 10 isn’t
divisible by 4 - NO
5: The last digit is 0 - YES
6: Divisible by 2 and 3 - YES
9: 8 + 1 + 0 = 9; 9 is divisible by 9 - YES
10: The last digit is 0 – YES
810 is divisible by 2, 3, 5, 6, 9, and 10
675
2: The last digit is odd - NO
3: 6 + 7 + 5 = 18; 18 is divisible by 3 - YES
4: The last two digits form the number 75. 75 is not
divisible by 4 - NO
5: The last digit is 5 - YES
6: Divisible by 3, but not by 2 - NO
9: 6 +7 + 5 = 18. 18 is divisible by 9 - YES
10: The last digit is 5 – NO
675 is divisible by 3, 5, and 9
Tell whether the statement is true or
false. Explain your answer.
• All even numbers are divisible by 2
• TRUE
Tell whether the statement is true or
false. Explain your answer.
• All odd numbers are divisible by 3
• FALSE
• 5 is an odd number. If the last digit is 5, then the
number is divisible by 5
Tell whether the statement is true or
false. Explain your answer.
• Some even numbers are divisible
by 5
• TRUE
• 0 is an even number. If the last digit is 0, then it
is divisible by 5.
Prime
or
Composite????
47
Prime: (1 x 47)
57
Composite: (is divisible by 3)
95
Composite: (divisible by 5)
97
Prime: (1 x 97)