Question

Which of the given options is the simplest form of $\frac{384}{512}$?

• A. 1/2
• B. 3/4
• C. 1/4
• D. 3/2

Answer 1

The correct option is B

3/4

Highest Common Factor (HCF) is the largest positive integer which divides two or more integers without any remainder. It is also called Greatest Common Divisor or Greatest Common Factor (GCF).
To simplify a fraction: Divide the numerator and the denominator by the greatest number that will divide both numbers exactly (HCF of both the numbers).

Factors of 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Factors of 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
The common factors are 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128.
Hence, HCF = 128

Dividing numerator and denominator by 128, we get
$\frac{384÷128}{512÷128}=\frac{3}{4}$

Hence, the simplest form of $\frac{384}{512}=\frac{3}{4}$.