A number when divided by 133 gives a remainder of 49. What is the remainder when the number is divided by 7?

The remainder when a number is divided by 133 is 49. This means that the number is 49 more than a multiple of 133.

Since 133 is a multiple of 7 (as 133 = 7*19), any multiple of 133 will also be a multiple of 7.

Therefore, when we add 49 (which gives a remainder of 0 when divided by 7) to a multiple of 133, the remainder when this number is divided by 7 will still be 0.

So, the remainder when the number is divided by 7 is 0.

Sure, let's solve this step by step.

1. Understand the problem:

   • We have a number $N$ which, when divided by 133, gives a remainder of 49.
   • We need to find the remainder when this same number $N$ is divided by 7.

2. Express the given condition mathematically:

   • When $N$ is divided by 133, the remainder is 49. This can be written as: $N = 133k + 49$ where $k$ is some integer.

3. Substitute $N$ in terms of $k$ and 49:

   • We need to find the remainder when $N$ is divided by 7. So, we substitute $N$ from the above equation: $N = 133k + 49$

4. Simplify the expression modulo 7:

   • We need to find $N \mod 7$. So, we take the equation modulo 7: $N \mod 7 = (133k + 49) \mod 7$

5. Break it down using properties of modulo:

   • We can use the property that $(a + b) \mod m = [(a \mod m) + (b \mod m)] \mod m$: $N \mod 7 = (133k \mod 7 + 49 \mod 7) \mod 7$

6. Calculate each term modulo 7:

   • First, find $133 \mod 7$: $133 \div 7 = 19 \text{ remainder } 0 \quad \text{(since 133 is exactly divisible by 7)}$ So, $133 \mod 7 = 0$.

   • Next, find $49 \mod 7$: $49 \div 7 = 7 \text{ remainder } 0 \quad \text{(since 49 is exactly divisible by 7)}$ So, $49 \mod 7 = 0$.

7. Combine the results:

   • Now, substitute back into the equation: $N \mod 7 = (0k + 0) \mod 7 = 0$

8. Conclusion:

   • The remainder when the number $N$ is divided by 7 is $0$.

So, the remainder when the number is divided by 7 is 0.

The remainder when a number is divided by 133 is 49. This means that the number is of the form 133n + 49, where n is the quotient.

Now, we need to find the remainder when this number is divided by 7.

We know that 133 is divisible by 7, with a quotient of 19. So, we can rewrite the number as (7*19n) + 49.

When this number is divided by 7, the first term (7*19n) will be completely divisible by 7, leaving no remainder.

So, the remainder when the number is divided by 7 will be the remainder when 49 is divided by 7.

Since 49 is completely divisible by 7, the remainder is 0.