# Divisibility for 64

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Show the divisibility for 64 in terms of 2,3,4,5,6,7,8,9,10,11

Divisibililty Check for 2
A number is divisible by 2 if the last digit ends in 0,2,4,6,8
The last digit of 64 is 4
Since 4 is equal to 0,2,4,6,8, then 64 is divisible by 2

Divisibililty Check for 3
A number is divisible by 3 if the sum of it's digits ends is divisible by 3
The sum of the digits for 64 is 6 + 4 = 10
Since 10 is not divisible by 3, then 64 is not divisible by 3

Divisibililty Check for 4
A number is divisible by 4 if the last two digits are divisible by 4
The last 2 digits of 64 are 64
Since 64 is divisible by 4, then 64 is divisible by 4

Divisibililty Check for 5
A number is divisible by 5 if it ends with a 0 or 5
The last digit of 64 is 4
Since 4 is not equal to 0 or 5, then 64 is not divisible by 5

Divisibililty Check for 6
A number is divisible by 6 if it is divisible by both 2 and 3
Since 64 is not divisible by 2 and 3, then 64 is not divisible by 6

Divisibililty Check for 7
To see if 64 is divisible by 7, we multiply each respective digit by 1,3,2,6,4,5 working backwards and repeat as necessary
4(1) + 6(3) = 23
Since 23 is not divisible by 7, then 64 is not divisible by 7

Divisibililty Check for 8
A number is divisible by 8 if the last three digits are divisible by 8
The last 2 digits of 64 are 64
Since 64 is divisible by 8, then 64 is divisible by 8

Divisibililty Check for 9
A number is divisible by 9 if the sum of it's digits is divisible by 9.
The sum of the digits for 64 is 6 + 4 = 10
Since 10 is not divisible by 9, then 64 is not divisible by 9

Divisibililty Check for 10
A number is divisible by 10 if it ends with a 0
The last digit of 64 is 4
Since 4 is not equal to 0, then 64 is not divisible by 10

Divisibililty Check for 11
A number is divisible by 11 if the sum of the odd digits - the sum of the even digits = 0 or is a multiple of 11
Sum the odd digits:
64
6
Odd Sum = 6

Sum the even digits:
64
4
Even Sum = 4

Take the difference of the odd sum and the even sum:
Δ = Odd Sum - Even Sum
Δ = 6 - 4
Δ = 2

Divisibility Check:
Because Δ / 11 is not an integer = 5.8, then 64 is NOT divisible by 11

In summary, 64 is divisible by (2,4,8)