Question

when 165 is divided by n remainder is 9 and when 495 is divided by n remainder is 27 , which can be value of n?

Answer 1

There is no value of n that satisfies both conditions.

Step-by-step explanation:

To find the value of n, we need to find a number that leaves a remainder of 9 when dividing into 165 and a remainder of 27 when dividing into 495. To find a common divisor, we can use the method of checking the remainders for a set of numbers. We can start by looking for divisors of 165 that leave a remainder of 9. After trying a few values, we find that 33 satisfies this condition. Next, we check if 33 also leaves a remainder of 27 when dividing into 495. Since 495 ÷ 33 = 15, which does not leave a remainder of 27, we know that 33 is not the value of n. Therefore, there is no value of n that satisfies both conditions.

Answer 2

The possible values of n are the factors of 156.

Step-by-step explanation:

Let's assume the value of n as x. We can set up two equations to represent the given information:

165 % x = 9 -----> Equation 1

495 % x = 27 -----> Equation 2

In Equation 1, the remainder when 165 is divided by n is 9. This can be written as an equation: 165 = x * q1 + 9, where q1 is the quotient. Let's simplify this equation by subtracting 9 from both sides: 165 - 9 = x * q1

156 = x * q1

Similarly, in Equation 2, the remainder when 495 is divided by n is 27. This can be written as an equation: 495 = x * q2 + 27, where q2 is the quotient. Simplifying this equation by subtracting 27 from both sides: 495 - 27 = x * q2

468 = x * q2

Now, we have two equations: 156 = x * q1 and 468 = x * q2. We can divide these equations to eliminate x: 156/468 = x * q1 / (x * q2)

1/3 = q1 / q2

Since q1 and q2 represent the quotients, they must be integers. The only way 1/3 can be expressed as the ratio of two integers is if q1 is a multiple of 1 and q2 is a multiple of 3. In other words, q1 can be any integer, but q2 must be a multiple of 3.

Therefore, the possible values of n are the factors of 156, which are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.