Can 252/1663 be simplified?

If it can be simplified, what is the new simplified fraction?

nboirog

Prime factors of 252 is 2x2x3x3x7. 1663 can not be divided by 2, 3 or 7 so it is in sipliest form.

To determine if the fraction 252/1663 can be simplified, we need to find the greatest common divisor (GCD) of the numerator (252) and the denominator (1663).

To find the GCD, we can use the Euclidean algorithm. The steps are as follows:

1. Divide the numerator (252) by the denominator (1663).
- 1663 ÷ 252 = 6 with a remainder of 71

2. Divide the previous denominator (252) by the remainder (71) from step 1.
- 252 ÷ 71 = 3 with a remainder of 39

3. Repeat step 2 until the remainder becomes 0.
- 71 ÷ 39 = 1 with a remainder of 32
- 39 ÷ 32 = 1 with a remainder of 7
- 32 ÷ 7 = 4 with a remainder of 4
- 7 ÷ 4 = 1 with a remainder of 3
- 4 ÷ 3 = 1 with a remainder of 1
- 3 ÷ 1 = 3 with no remainder
- Since the remainder is now 0, we stop here.

The GCD of 252 and 1663 is 1 since it is the last non-zero remainder in the Euclidean algorithm.

Since the GCD is 1, it means that 252/1663 cannot be simplified any further. Therefore, the fraction 252/1663 is already in its simplest form.