What is the simplest form of the fraction when 724 is divided by 3548?

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To simplify the fraction of 724 divided by 3548, we start by expressing it as:

Fraction: 724 / 3548

Next, we will find the greatest common divisor (GCD) of 724 and 3548 to reduce the fraction to its simplest form. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.

Using the Euclidean algorithm:

  1. First, compute 3548 mod 724, which gives us the remainder when 3548 is divided by 724.
  2. Keep applying the Euclidean algorithm until the remainder becomes zero.

After going through the calculations, we find:

  • The GCD of 724 and 3548 is 4.

Now we can divide both the numerator and the denominator by their GCD:

  • 724 ÷ 4 = 181
  • 3548 ÷ 4 = 887

Thus, the fraction can be simplified to:

Simplified Fraction: 181 / 887

This fraction, 181 / 887, is in its lowest terms, as there are no common factors between 181 and 887 other than 1.

In conclusion, when you divide 724 by 3548 and reduce it to the lowest fraction, the result is:

Final Answer: 181 / 887

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