Asked by Anonymous
the product of 4 consecutive even number is always divisible by
Answers
Answered by
Steve
well, the numbers are
2k 2k+2 2k+4 2k+6
multiply them and you have
2^4(k(k+1)(k+2)(k+3))
Now, two of those numbers must be even, so the product is divisible by 2^6
In addition, the product of 3 consecutive numbers is divisible by 6, so
2^7*3 = 384 divides
2k 2k+2 2k+4 2k+6
multiply them and you have
2^4(k(k+1)(k+2)(k+3))
Now, two of those numbers must be even, so the product is divisible by 2^6
In addition, the product of 3 consecutive numbers is divisible by 6, so
2^7*3 = 384 divides
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