multiply consecutive even positive integers until product[2*4*6] is divisible by 1992.largest even no.is????

Answer 1

The prime factors of 1992 are 2 x 2 x 2 x 3 x 83.

By including 2 * 4 * 6, you have already covered 2 x 2 x 2 x 3, but you need to cover 83. 83 is prime, so the first time you have an even number that has 83 as a factor will be 166 (2 * 83).

That means you must figure the product of 2 * 4 * 6 * ... * 164 * 166 for it to be divisible by 1992.

The answer is largest even number in the product is 166.

Answer 2

1992 = 2*2*2*249
= 2*2*2*3*83
we need to take alleast 83 numbers so that 83 is covered

if we take upto 83 3 is also covered

so number of terms = 83 largest even number = 2*83

we required atleast 3 2's and number of 2s > 83

so largest number = 2*83 or 166

Answer 3

1992 is factorized as 2*2*2*249
i dont factorize 249 bcos it is odd
now 2*4*6*.... will not be divisible by 1992 until we have the 249 term
so the largest number is 249*2 = 498