Question

Find a number between 500 and 600 which is divisible by 17,34 and 51:​

Answer 1

Answer:

510 is answer

17*30

34*15

51*10

Answer 2

Step-by-step explanation:

between 500 and 600, only 3-digit number lies.

For 17:

Divisibility rule of 17 for 3-digit number is if you subtract the (5×last-digit) from remaining digits you will be left with 17. example 221: 22 - (5×1) = 17.

so, lets take any two digit number between 50 and 60, eg. 51.

so number that is divisible by 17 is 51x.

so, 51 - 5x = 17,

-5x = 17-51

-5x = -34

x = $\frac{-35}{-5}$ = 7

so a number between 500 and 600 divisible by 17 is 527.

but there are many like 510,527,544,561,578,595.

For 34:

every number divisible by 34 is divisible by 17 and 2 (as 17×2 = 34), but ever number divisible by 17 and 2 is not divisible by 34

And, 510 is one of them which is divisible by both 17 and 2 and also by 34.

but there are two more numbers that are, 544 and 578 between 500 and 600.

For 51:

every number divisible by 51 is divisible by 17 and 3 (as 17×3 = 54), but ever number divisible by 17 and 3 is not divisible by 51.

there are two number between 500 and 600 that are divisible by 51, 510 and 561.

But 510 is a common divisible of 17, 34 and 51.

so answer to your question is 510.