Question

4 Digit Largest Narcissistic Number which divisible by 4

Answer 1

Answer:

Prime factorisation of 12=2

2

×3

Prime factorisation of 16=2

4

Prime factorisation of 24=2

3

×3

Prime factorisation of 40=2

3

×5

So, LCM of 12,16,24,40=2

4

×3×5=240

Multiples of 240 are also multiples of all of these given numbers

So, 240,480,720,960,1200... are all multiples of 12,16,24,40

Of these, as 1200 is the smallest 4− digit number divisible by 12,16,24,40, the number 1200+12=1212 will be exactly divisible by these numbers when lessened by 12

The highest 4− digit number is 9999.

9999 when divided by 240 gives a remainder 159, so 9999−159=9840 is the largest 4− digit number divisible by 12,16,24,40,

And the number 9840+12=9852 will be exactly divisible by these numbers when lessened by 12