Question

how many numbers between 200 and 600 are divisible by 4,5 & 6?

Answer 1

★★★hey friend!!!!★★★
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⇒ here is urs answer!!

Let’s firstly drop some rules of divisibility by 4, 5 and 6:

→ by 4: The last two digits are divisible by 4
→ by 5: The last digit is either a 0 or a 5
→ by 6: The number is even (divisible by two) and its sum is divisible by three (divisible by three)

⇒ Now, if the last two digits are divisible by 4, they will not end in a 5. Therefore, we are left with the possible terminations for our numbers:

→ 00
→ 20
→ 40
→ 60
→ 80

⇒ We just need to choose the first digit so that the sum of the digits is divisible by 3. That yelds this:

⇒ 00→3or6
⇒ 40→2
⇒ 60→3
⇒ 80→5

This means that there are 6 numbers between 200 and 600 which are simultaneously divisible by 4, 5 and 6
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★★★hope this may help you!!★★★

Answer 2

Hey,sup!

As per the question,

HCF of 4,5,6 is 60.

So first term(a)= 240 (in the range which is divisible by 60.
Last term(l)= 600 ( in the range which is divisible by 60.
difference(d)= 60.

=>T(n)=a+(n-1)d.
=>600=240+(n-1)60.
=>600-240=(n-1)60.
=>360=(n-1)60.
=>n-1=360/60.
=>n-1=6.
=>n=6+1=7.
So,there are 7 numbers between 200 to 600 that are divisible by 4,5,6.
Hope it helps.