Lecture20.notebook
March 13, 2017
Lecture20.notebook
March 13, 2017
85 has 5 as its one's digit, so it is not divisible by 2.
129734 has 4 as its one's digit, so it is divisible by 2.
4760 has 0 as its one's digit, so it is divisible by 2.
Lecture20.notebook
March 13, 2017
85 has 5 as its one's digit, so it is divisible by 5.
129734 has 4 as its one's digit, so it is not divisible by 5.
4760 has 0 as its one's digit, so it is divisible by 5.
Lecture20.notebook
March 13, 2017
85 has 5 as its one's digit, so it is not divisible by 10.
129734 has 4 as its one's digit, so it is not divisible by 10.
4760 has 0 as its one's digit, so it is divisible by 10.
Lecture20.notebook
March 13, 2017
Since 34 is not divisible by 4, 129734 is not divisible by 4.
Since 60 is divisible by 4, 4760 is divisible by 4.
4760 = 47(100) + 60
Lecture20.notebook
March 13, 2017
Since 132 is not divisible by 8, 129132 is not divisible by 8.
Since 160 is divisible by 8, 3160 is divisible by 8.
Lecture20.notebook
March 13, 2017
Since 7 + 8 = 15 is divisible by 3, then 78 is divisible by 3.
Since 1 + 2 + 3 + 4 = 10 is not divisible by 3, then 1234 is not divisible by 3.
Since 4 + 8 + 1 + 2 + 0 + 4 = 19 is not divisible by 3, then 481204 is not divisible by 3.
Lecture20.notebook
March 13, 2017
Since 7 + 8 = 15 is not divisible by 9, then 78 is not divisible by 9.
Since 3 + 1 + 5 + 6 = 15 is not divisible by 9, then 3156 is not divisible by 9.
Since 4 + 8 + 1 + 2 + 0 + 4 = 19 is not divisible by 9, then 481204 is not divisible by 9.
Lecture20.notebook
March 13, 2017
a. Since the one's digit of 78 is 8, then 78 is divisible by 2.
b. Since 7 + 8 = 15 is divisible by 3, then 78 is divisible by 3.
Therefore, since 78 is divisible by both 2 and 3, it is divisible by 6.
a. Since the one's digit of 3165 is 5, then 3165 is not divisible by 2.
Therefore, it is not divisible by 6.
a. Since the one's digit of 10248 is 8, then 10248 is divisible by 2.
b. Since 1 + 0 + 2+ 4 + 8 = 15 is divisible by 3, then 10248 is divisible by 3.
Therefore, since 10248 is divisible by both 2 and 3, it is divisible by 6.
Lecture20.notebook
March 13, 2017
a. Since 78 is not divisible by 4, then 78 is not divisible by 4.
Therefore, 78 is not divisible by 12.
a. Since 56 is divisible by 4, then 3156 is divisible by 4.
b. Since 3 + 1 + 5 + 6 = 15 is divisible by 3, then 3156 is divisible by 3.
Therefore, since 3156 is divisible by both 4 and 3, it is divisible by 12.
Lecture20.notebook
March 13, 2017
Since 7 + 7 = 14 and 8 + 6 = 14 with 14 ­ 14 = 0 which is divisible by 11, so the number 7876 is divisible by 11.
Since 2 + 6 + 9 = 17 and 1 + 1 + 3 = 5 with 17 ­ 5 = 12 which is not divisible by 11, so the number 216193 is not divisible by 11.
Lecture20.notebook
March 13, 2017