When the fraction 64/12 is reduced completely to its simplest form by cancelling all common factors of the numerator and denominator, what is the resulting simplified fraction?

Introduction / Context:
This question assesses basic fraction simplification, an essential arithmetic skill. A fraction is in simplest form when the numerator and denominator share no common factor greater than 1. Here, we are given 64/12 and asked to reduce it fully. Many aptitude tests use such questions to check comfort with highest common factor ideas and cancellation of common factors.

Given Data / Assumptions:
- Original fraction = 64/12.
- We are asked to express it in simplest form.
- Simplest form means numerator and denominator are coprime (no common factor beyond 1).
- Only positive fractions are considered here, so we do not worry about signs.

Concept / Approach:
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and denominator and divide both by that value. For 64 and 12, we identify the largest integer that divides both numbers exactly. Factoring or repeated division by common primes such as 2 can help us quickly reach the simplified fraction.

Step-by-Step Solution:
Start with 64/12. Both 64 and 12 are even, so divide numerator and denominator by 2. 64 / 2 = 32, 12 / 2 = 6, giving 32/6. 32 and 6 are still even, so divide again by 2. 32 / 2 = 16, 6 / 2 = 3, giving 16/3. Now 16 and 3 have no common factor greater than 1, so 16/3 is in simplest form.

Verification / Alternative check:
We can use prime factors. 64 = 2^6 and 12 = 2^2 * 3. Cancelling 2^2 from numerator and denominator leaves 2^4 / 3 which equals 16/3. This matches the stepwise simplification and confirms our answer.

Why Other Options Are Wrong:
Option 19/6 does not equal 64/12 when converted to decimals or compared via cross multiplication.
Option 32/4 simplifies further to 8, so it is not equal to 64/12 and is not in simplest form for this fraction.
Option “None of the above” is incorrect because we have identified a correct simplified fraction among the choices, namely 16/3.

Common Pitfalls:
Some learners stop simplification after only one division step, such as 64/12 to 32/6, and forget to reduce further. Others might divide numerator and denominator by a wrong common factor that does not divide both numbers. Remember to keep checking for common factors until no further cancellation is possible.

Final Answer:
The fraction 64/12, when reduced to its simplest form, becomes 16/3.