Question

Find the greatest number of 5-digits exactly divisible by 2, 4, 6,8,10​

Answer 1

Answer:

99960

Step-by-step explanation:

In number theory remember one fact every positive integer is a multiple of prime number(s) else it can't exist.

The Least Common Multiple of these 5 digits (2,4,6,8,10) is the multiple of highest power of every prime number that occurs in the set (2,4,6,8,10).

So 2 has just 1 prime factor 2 itself

4 has prime factor 2 raised to the power 2 times i.e  22

6 has prime factors 2,3 each to the power 1

8 has prime factor 2 raised to the power 3 times i.e  23

10 has prime factors 2 and 5 each to the power 1 time.

So all the prime numbers that occured are 2, 3, 5 with factors powers 3, 1, 1 so Least common multiple is  23x31x51  = 8 x 3 x 5 = 120.

So the highest 5 digit number divisible by the set (2,4,6,8,10) should also be a multiple of 120. We know the highest 5 digit number is 10000 i.e  104 . So just divide and see the remainder, that would be the highest divisible 5 digit number as Pallv Sahu mentioned 99960

Answer 2

Answer:

99960

Step-by-step explanation:

LCM of 2 4 6 8 10 = 120

greatest 5 digits no. = 99999

Therefore , divide 99999 by 120

Reminder = 39

Now , subtract 39 from 99999

(99999 - 39) = 99960