# Largest factor of consecutive natural numbers

• Sep 7th 2009, 03:26 AM
guru
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?
• Sep 7th 2009, 05:24 AM
mr fantastic
Quote:

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).
• Sep 7th 2009, 07:32 AM
integerfan
Quote:

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
• Sep 8th 2009, 01:12 AM
guru
thanks