Posted by Lyndse on Saturday, September 26, 2009 at 10:23am.
True or fals: a number is divisible by 8 if it is divisble by 4 and divisible by 2?
And how many variations of 3_2_ are divisible by six?

Math  MathMate, Saturday, September 26, 2009 at 6:58pm
"True or fals: a number is divisible by 8 if it is divisble by 4 and divisible by 2?"
False.
This logic works if the two numbers are prime to each other, i.e. there are no common factors between the two numbers.
For example, it is true to say that a number is divisible by 6 if it is divisible by 3 and divisible by 2.
If the number 3A2B needs to be divisible by 6 (where A and B stand for undertermined digits), then it has to be divisible by 3 and divisible by 2.
The rule of divisibility for 2 is that the last digit (B) must be even.
The rule of divisibility for 3 is that the sum of all digits must be divisible by 3.
So enumerate the possibilities for A for each possible value of B, as follows:
A=0
B=1 (3120), B=4 (3420) B=7 (3720)
A=2
B=2 (3222), B=5 (3522) B=8 (3822)
A=4
...
A=6
...
A=8
...
How many variations are possible?
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