Question

Find the greatest number of four digits which is exactly divisible by 16,24,28,35

Answer 1

LCM of 16, 24, 28 and 35 is 1680.
Greatest number of 4- digits is 9999.
(Divide 9999 by 1680)
The remainder is 1599.
Required number= 9999 - 1599
= 8400
Ans.=8400 is the greatest number of 4- digits that is exactly divisible by 16,24,28 and 35.

Answer 2

Greatest 4-digit number exactly divisible by the given divisors is 8400

GIVEN

Divisor = 16,24,28,35

TO FIND

Greatest 4-digit number exactly divisible by the given divisors.

SOLUTION

We can simply solve the above problem as follows;

To calculate the number exactly divisible by 16,24,28,35 we will first calculate the LCM of the given number

2 |16, 24, 28, 35

2 |4, 12, 14, 35

2 |2, 6, 7, 35

2|1, 3, 7, 35

3 |1, 1, 7, 35

7 |1, 1, 1, 5

5 |1, 1, 1, 1

LCM = 2×2×2×2×3×5×7 = 1680

Now, This is the smallest 4-digit number exactly divisible by the given numbers.

We know that the highest 4-digit number is 9999

Number divisible by given numbers = 9999/1680

The remainder is 8400.

Hence, Greatest 4-digit number exactly divisible by the given divisors is 8400

#Spj2