# Thread: Largest factor of consecutive natural numbers

1. ## Largest factor of consecutive natural numbers

the largest natural number which exactly divides the product of any 4 consecutive natural number AES is

a)6 b)12 c)24 d)120

how i solve this problem?

2. Originally Posted by guru
the largest natural number which exactly divides the product of any 4 consecutive natural number AES is

a)6 b)12 c)24 d)120

how i solve this problem?
The correct answer obviously has to divide (1)(2)(3)(4).

3. Originally Posted by guru
the largest natural number which exactly divides the product of any 4 consecutive natural number AES is

a)6 b)12 c)24 d)120

how i solve this problem?
say a,b,c,d are the consecutive numbers. Among them,
there are two even numbers definetly. by the same reasoning,
there is at least one number divisible by 3 and
there is exactly one number divisible by 4.
thus, numbers 2,3 and 4 have their representatives (multiples) contributing to the product.
hence 2*3*4=24 should divide a*b*c*d

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# The largest natural number which exactly divides the product of any four consecutive natural numbers

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