Respuesta :
Answer:
We need to check by how many numbers 504 is divisible from 2, 3, 5, 7, 11
Let us consider each number one by one.
For number 2:
We know that all even numbers are divisible by 2.
So, 504 is divisible by 2.
For number 3:
We know that for a number to be divisible by 3, the sum of the digits need to be divisible by 3.
The sum of the digits of number 504 is 9, which is divisible by 3, 504 is divisible by 3.
So, 504 is divisible by 3.
For number 5:
We know that for a number to be divisible by 5, the unit digit of the number needs to be 0 or 5. The digit for the number 504 is 4, which is not 0 or 5.
So, 504 is not divisible by 5.
For number 7:
We know that for a number to be divisible by 7, We need to double the digit at the unit place and subtract it from the number formed by the remaining digit, if the result obtained is divisible by 7, the number is divisible by 7.
In 504 the digit at the unit place is 4.
Double of 4 is 8, and the number formed by the remaining digit is 50. Now, on subtracting 8 from 50 we get 42, which is divisible by 7.
So, 504 is divisible by 7.
For number 11:
We know that for a number to be divisible by 7, we need to find the sum of the numbers that occupy the even places and the sum of the numbers that occupy the odd places and if the difference of sum of even places and odd places is 0 or multiple of 11, the number will be divisible by 11.
Now, in 504, the digit at the even places is 0. So sum is 0.
The digit at the odd places is 5 and 4. So, sum is 9.
Now, the difference is [tex]9-0=9[/tex], which is not 0 or multiple of 11.
So, 504 is not divisible by 11.
In 504 the digit at the unit place is 4.
Double of 4 is 8, and the number formed by the remaining digit is 50. Now, on subtracting 8 from 50 we get 42, which is divisible by 7.
So, 504 is divisible by 7.
Hence, from the given numbers, we have numbers 2, 3, 7 by which 504 is divisible and the numbers 5 and 11 by which the number is not divisible.
